Solve for y 4(1-y)=5(1+2y)+9

$4 (1 - y) = 5 (1 + 2 y) + 9$

Simplify $4 (1 - y)$ .

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Apply the distributive property.

$4 \cdot 1 + 4 (- y) = 5 (1 + 2 y) + 9$

Multiply.

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Multiply $4$ by $1$ .

$4 + 4 (- y) = 5 (1 + 2 y) + 9$

Multiply $- 1$ by $4$ .

$4 - 4 y = 5 (1 + 2 y) + 9$

Simplify $5 (1 + 2 y) + 9$ .

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Simplify each term.

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Apply the distributive property.

$4 - 4 y = 5 \cdot 1 + 5 (2 y) + 9$

Multiply $5$ by $1$ .

$4 - 4 y = 5 + 5 (2 y) + 9$

Multiply $2$ by $5$ .

$4 - 4 y = 5 + 10 y + 9$

Add $5$ and $9$ .

$4 - 4 y = 10 y + 14$

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

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Subtract $10 y$ from both sides of the equation.

$4 - 4 y - 10 y = 14$

Subtract $10 y$ from $- 4 y$ .

$4 - 14 y = 14$

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

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Subtract $4$ from both sides of the equation.

$- 14 y = 14 - 4$

Subtract $4$ from $14$ .

$- 14 y = 10$

Divide each term by $- 14$ and simplify.

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Divide each term in $- 14 y = 10$ by $- 14$ .

$\frac{- 14 y}{- 14} = \frac{10}{- 14}$

Cancel the common factor of $- 14$ .

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Cancel the common factor.

$\frac{- 14 y}{- 14} = \frac{10}{- 14}$

Divide $y$ by $1$ .

$y = \frac{10}{- 14}$

Simplify $\frac{10}{- 14}$ .

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Cancel the common factor of $10$ and $- 14$ .

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Factor $2$ out of $10$ .

$y = \frac{2 (5)}{- 14}$

Cancel the common factors.

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Factor $2$ out of $- 14$ .

$y = \frac{2 \cdot 5}{2 \cdot - 7}$

Cancel the common factor.

$y = \frac{2 \cdot 5}{2 \cdot - 7}$

Rewrite the expression.

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

Move the negative in front of the fraction.

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

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$y = - 0.\overline{714285}$

Solve for y 4(1-y)=5(1+2y)+9

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