Solve for p -12029/1470+11p=1/5*(-23/6p-5/6)

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{23}{6} p - \frac{5}{6})$

Simplify $\frac{1}{5} \cdot (- \frac{23}{6} p - \frac{5}{6})$ .

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Simplify each term.

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Combine $p$ and $\frac{23}{6}$ .

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{p \cdot 23}{6} - \frac{5}{6})$

Move $23$ to the left of $p$ .

$- \frac{12029}{1470} + 11 p = \frac{1}{5} \cdot (- \frac{23 p}{6} - \frac{5}{6})$

Apply the distributive property.

$- \frac{12029}{1470} + 11 p = \frac{1}{5} (- \frac{23 p}{6}) + \frac{1}{5} (- \frac{5}{6})$

Multiply $\frac{1}{5} (- \frac{23 p}{6})$ .

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Multiply $\frac{1}{5}$ and $\frac{23 p}{6}$ .

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{5 \cdot 6} + \frac{1}{5} (- \frac{5}{6})$

Multiply $5$ by $6$ .

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} (- \frac{5}{6})$

Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{6}$ into the numerator.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} \cdot \frac{- 5}{6}$

Factor $5$ out of $- 5$ .

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} \cdot \frac{5 (- 1)}{6}$

Cancel the common factor.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{1}{5} \cdot \frac{5 \cdot - 1}{6}$

Rewrite the expression.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} + \frac{- 1}{6}$

Move the negative in front of the fraction.

$- \frac{12029}{1470} + 11 p = - \frac{23 p}{30} - \frac{1}{6}$

Move all terms containing $p$ to the left side of the equation.

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Add $\frac{23 p}{30}$ to both sides of the equation.

$- \frac{12029}{1470} + 11 p + \frac{23 p}{30} = - \frac{1}{6}$

To write $11 p$ as a fraction with a common denominator, multiply by $\frac{30}{30}$ .

$- \frac{12029}{1470} + 11 p \cdot \frac{30}{30} + \frac{23 p}{30} = - \frac{1}{6}$

Combine $11 p$ and $\frac{30}{30}$ .

$- \frac{12029}{1470} + \frac{11 p \cdot 30}{30} + \frac{23 p}{30} = - \frac{1}{6}$

Combine the numerators over the common denominator.

$- \frac{12029}{1470} + \frac{11 p \cdot 30 + 23 p}{30} = - \frac{1}{6}$

Simplify each term.

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Simplify the numerator.

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Factor $p$ out of $11 p \cdot 30 + 23 p$ .

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Factor $p$ out of $11 p \cdot 30$ .

$- \frac{12029}{1470} + \frac{p (11 \cdot 30) + 23 p}{30} = - \frac{1}{6}$

Factor $p$ out of $23 p$ .

$- \frac{12029}{1470} + \frac{p (11 \cdot 30) + p \cdot 23}{30} = - \frac{1}{6}$

Factor $p$ out of $p (11 \cdot 30) + p \cdot 23$ .

$- \frac{12029}{1470} + \frac{p (11 \cdot 30 + 23)}{30} = - \frac{1}{6}$

Multiply $11$ by $30$ .

$- \frac{12029}{1470} + \frac{p (330 + 23)}{30} = - \frac{1}{6}$

Add $330$ and $23$ .

$- \frac{12029}{1470} + \frac{p \cdot 353}{30} = - \frac{1}{6}$

Move $353$ to the left of $p$ .

$- \frac{12029}{1470} + \frac{353 p}{30} = - \frac{1}{6}$

Move all terms not containing $p$ to the right side of the equation.

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Add $\frac{12029}{1470}$ to both sides of the equation.

$\frac{353 p}{30} = - \frac{1}{6} + \frac{12029}{1470}$

To write $- \frac{1}{6}$ as a fraction with a common denominator, multiply by $\frac{245}{245}$ .

$\frac{353 p}{30} = - \frac{1}{6} \cdot \frac{245}{245} + \frac{12029}{1470}$

Write each expression with a common denominator of $1470$ , by multiplying each by an appropriate factor of $1$ .

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Multiply $\frac{1}{6}$ and $\frac{245}{245}$ .

$\frac{353 p}{30} = - \frac{245}{6 \cdot 245} + \frac{12029}{1470}$

Multiply $6$ by $245$ .

$\frac{353 p}{30} = - \frac{245}{1470} + \frac{12029}{1470}$

Combine the numerators over the common denominator.

$\frac{353 p}{30} = \frac{- 245 + 12029}{1470}$

Add $- 245$ and $12029$ .

$\frac{353 p}{30} = \frac{11784}{1470}$

Cancel the common factor of $11784$ and $1470$ .

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Factor $6$ out of $11784$ .

$\frac{353 p}{30} = \frac{6 (1964)}{1470}$

Cancel the common factors.

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Factor $6$ out of $1470$ .

$\frac{353 p}{30} = \frac{6 \cdot 1964}{6 \cdot 245}$

Cancel the common factor.

$\frac{353 p}{30} = \frac{6 \cdot 1964}{6 \cdot 245}$

Rewrite the expression.

$\frac{353 p}{30} = \frac{1964}{245}$

Multiply both sides of the equation by $\frac{30}{353}$ .

$\frac{30}{353} \cdot \frac{353 p}{30} = \frac{30}{353} \cdot \frac{1964}{245}$

Simplify both sides of the equation.

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Simplify $\frac{30}{353} \cdot \frac{353 p}{30}$ .

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Cancel the common factor of $30$ .

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Cancel the common factor.

$\frac{30}{353} \cdot \frac{353 p}{30} = \frac{30}{353} \cdot \frac{1964}{245}$

Rewrite the expression.

$\frac{1}{353} \cdot (353 p) = \frac{30}{353} \cdot \frac{1964}{245}$

Cancel the common factor of $353$ .

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Factor $353$ out of $353 p$ .

$\frac{1}{353} \cdot (353 (p)) = \frac{30}{353} \cdot \frac{1964}{245}$

Cancel the common factor.

$\frac{1}{353} \cdot (353 p) = \frac{30}{353} \cdot \frac{1964}{245}$

Rewrite the expression.

$p = \frac{30}{353} \cdot \frac{1964}{245}$

Simplify $\frac{30}{353} \cdot \frac{1964}{245}$ .

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Cancel the common factor of $5$ .

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Factor $5$ out of $30$ .

$p = \frac{5 (6)}{353} \cdot \frac{1964}{245}$

Factor $5$ out of $245$ .

$p = \frac{5 \cdot 6}{353} \cdot \frac{1964}{5 \cdot 49}$

Cancel the common factor.

$p = \frac{5 \cdot 6}{353} \cdot \frac{1964}{5 \cdot 49}$

Rewrite the expression.

$p = \frac{6}{353} \cdot \frac{1964}{49}$

Multiply $\frac{6}{353}$ and $\frac{1964}{49}$ .

$p = \frac{6 \cdot 1964}{353 \cdot 49}$

Multiply.

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Multiply $6$ by $1964$ .

$p = \frac{11784}{353 \cdot 49}$

Multiply $353$ by $49$ .

$p = \frac{11784}{17297}$

The result can be shown in multiple forms.

Exact Form:

$p = \frac{11784}{17297}$

Decimal Form:

$p = 0.68127420 \dots$

Solve for p -12029/1470+11p=1/5*(-23/6p-5/6)

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