Solve for y -4y-4/3=7/5y+7/3

$- 4 y - \frac{4}{3} = \frac{7}{5} y + \frac{7}{3}$

Combine $\frac{7}{5}$ and $y$ .

$- 4 y - \frac{4}{3} = \frac{7 y}{5} + \frac{7}{3}$

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

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Subtract $\frac{7 y}{5}$ from both sides of the equation.

$- 4 y - \frac{4}{3} - \frac{7 y}{5} = \frac{7}{3}$

To write $- 4 y$ as a fraction with a common denominator, multiply by $\frac{5}{5}$ .

$- 4 y \cdot \frac{5}{5} - \frac{7 y}{5} - \frac{4}{3} = \frac{7}{3}$

Combine $- 4 y$ and $\frac{5}{5}$ .

$\frac{- 4 y \cdot 5}{5} - \frac{7 y}{5} - \frac{4}{3} = \frac{7}{3}$

Combine the numerators over the common denominator.

$\frac{- 4 y \cdot 5 - 7 y}{5} - \frac{4}{3} = \frac{7}{3}$

Simplify each term.

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Simplify the numerator.

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Factor $y$ out of $- 4 y \cdot 5 - 7 y$ .

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Factor $y$ out of $- 4 y \cdot 5$ .

$\frac{y (- 4 \cdot 5) - 7 y}{5} - \frac{4}{3} = \frac{7}{3}$

Factor $y$ out of $- 7 y$ .

$\frac{y (- 4 \cdot 5) + y \cdot - 7}{5} - \frac{4}{3} = \frac{7}{3}$

Factor $y$ out of $y (- 4 \cdot 5) + y \cdot - 7$ .

$\frac{y (- 4 \cdot 5 - 7)}{5} - \frac{4}{3} = \frac{7}{3}$

Multiply $- 4$ by $5$ .

$\frac{y (- 20 - 7)}{5} - \frac{4}{3} = \frac{7}{3}$

Subtract $7$ from $- 20$ .

$\frac{y \cdot - 27}{5} - \frac{4}{3} = \frac{7}{3}$

Move $- 27$ to the left of $y$ .

$\frac{- 27 \cdot y}{5} - \frac{4}{3} = \frac{7}{3}$

Move the negative in front of the fraction.

$- \frac{27 y}{5} - \frac{4}{3} = \frac{7}{3}$

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

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Add $\frac{4}{3}$ to both sides of the equation.

$- \frac{27 y}{5} = \frac{7}{3} + \frac{4}{3}$

Combine the numerators over the common denominator.

$- \frac{27 y}{5} = \frac{7 + 4}{3}$

Add $7$ and $4$ .

$- \frac{27 y}{5} = \frac{11}{3}$

Multiply both sides of the equation by $- \frac{5}{27}$ .

$- \frac{5}{27} \cdot (- \frac{27 y}{5}) = - \frac{5}{27} \cdot \frac{11}{3}$

Simplify both sides of the equation.

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Simplify $- \frac{5}{27} \cdot (- \frac{27 y}{5})$ .

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Cancel the common factor of $5$ .

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Move the leading negative in $- \frac{5}{27}$ into the numerator.

$\frac{- 5}{27} \cdot (- \frac{27 y}{5}) = - \frac{5}{27} \cdot \frac{11}{3}$

Move the leading negative in $- \frac{27 y}{5}$ into the numerator.

$\frac{- 5}{27} \cdot \frac{- 27 y}{5} = - \frac{5}{27} \cdot \frac{11}{3}$

Factor $5$ out of $- 5$ .

$\frac{5 (- 1)}{27} \cdot \frac{- 27 y}{5} = - \frac{5}{27} \cdot \frac{11}{3}$

Cancel the common factor.

$\frac{5 \cdot - 1}{27} \cdot \frac{- 27 y}{5} = - \frac{5}{27} \cdot \frac{11}{3}$

Rewrite the expression.

$\frac{- 1}{27} \cdot (- 27 y) = - \frac{5}{27} \cdot \frac{11}{3}$

Cancel the common factor of $27$ .

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Factor $27$ out of $- 27 y$ .

$\frac{- 1}{27} \cdot (27 (- y)) = - \frac{5}{27} \cdot \frac{11}{3}$

Cancel the common factor.

$\frac{- 1}{27} \cdot (27 (- y)) = - \frac{5}{27} \cdot \frac{11}{3}$

Rewrite the expression.

$- 1 \cdot (- y) = - \frac{5}{27} \cdot \frac{11}{3}$

Multiply.

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Multiply $- 1$ by $- 1$ .

$1 \cdot y = - \frac{5}{27} \cdot \frac{11}{3}$

Multiply $y$ by $1$ .

$y = - \frac{5}{27} \cdot \frac{11}{3}$

Multiply $- \frac{5}{27} \cdot \frac{11}{3}$ .

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Multiply $\frac{11}{3}$ and $\frac{5}{27}$ .

$y = - \frac{11 \cdot 5}{3 \cdot 27}$

Multiply $11$ by $5$ .

$y = - \frac{55}{3 \cdot 27}$

Multiply $3$ by $27$ .

$y = - \frac{55}{81}$

The result can be shown in multiple forms.

Exact Form:

$y = - \frac{55}{81}$

Decimal Form:

$y = - 0.67901234 \dots$

Solve for y -4y-4/3=7/5y+7/3

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