Solve for y (9y+4)/3=(5y-4)/6+15

$\frac{9 y + 4}{3} = \frac{5 y - 4}{6} + 15$

Multiply both sides of the equation by $3$ .

$9 y + 4 = (\frac{5 y - 4}{6} + 15) \cdot (3)$

Remove parentheses.

$9 y + 4 = (\frac{5 y - 4}{6} + 15) \cdot (3)$

Simplify $(\frac{5 y - 4}{6} + 15) \cdot (3)$ .

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To write $15$ as a fraction with a common denominator, multiply by $\frac{6}{6}$ .

$9 y + 4 = (\frac{5 y - 4}{6} + 15 \cdot \frac{6}{6}) \cdot 3$

Simplify terms.

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Combine $15$ and $\frac{6}{6}$ .

$9 y + 4 = (\frac{5 y - 4}{6} + \frac{15 \cdot 6}{6}) \cdot 3$

Combine the numerators over the common denominator.

$9 y + 4 = \frac{5 y - 4 + 15 \cdot 6}{6} \cdot 3$

Simplify the numerator.

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Multiply $15$ by $6$ .

$9 y + 4 = \frac{5 y - 4 + 90}{6} \cdot 3$

Add $- 4$ and $90$ .

$9 y + 4 = \frac{5 y + 86}{6} \cdot 3$

Cancel the common factor of $3$ .

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Factor $3$ out of $6$ .

$9 y + 4 = \frac{5 y + 86}{3 (2)} \cdot 3$

Cancel the common factor.

$9 y + 4 = \frac{5 y + 86}{3 \cdot 2} \cdot 3$

Rewrite the expression.

$9 y + 4 = \frac{5 y + 86}{2}$

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

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Subtract $\frac{5 y + 86}{2}$ from both sides of the equation.

$9 y + 4 - \frac{5 y + 86}{2} = 0$

To write $9 y$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$9 y \cdot \frac{2}{2} - \frac{5 y + 86}{2} + 4 = 0$

Combine $9 y$ and $\frac{2}{2}$ .

$\frac{9 y \cdot 2}{2} - \frac{5 y + 86}{2} + 4 = 0$

Combine the numerators over the common denominator.

$\frac{9 y \cdot 2 - (5 y + 86)}{2} + 4 = 0$

Simplify the numerator.

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Multiply $2$ by $9$ .

$\frac{18 y - (5 y + 86)}{2} + 4 = 0$

Apply the distributive property.

$\frac{18 y - (5 y) - 1 \cdot 86}{2} + 4 = 0$

Multiply $5$ by $- 1$ .

$\frac{18 y - 5 y - 1 \cdot 86}{2} + 4 = 0$

Multiply $- 1$ by $86$ .

$\frac{18 y - 5 y - 86}{2} + 4 = 0$

Subtract $5 y$ from $18 y$ .

$\frac{13 y - 86}{2} + 4 = 0$

To write $4$ as a fraction with a common denominator, multiply by $\frac{2}{2}$ .

$\frac{13 y - 86}{2} + 4 \cdot \frac{2}{2} = 0$

Combine $4$ and $\frac{2}{2}$ .

$\frac{13 y - 86}{2} + \frac{4 \cdot 2}{2} = 0$

Combine the numerators over the common denominator.

$\frac{13 y - 86 + 4 \cdot 2}{2} = 0$

Simplify the numerator.

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Multiply $4$ by $2$ .

$\frac{13 y - 86 + 8}{2} = 0$

Add $- 86$ and $8$ .

$\frac{13 y - 78}{2} = 0$

Factor $13$ out of $13 y - 78$ .

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Factor $13$ out of $13 y$ .

$\frac{13 (y) - 78}{2} = 0$

Factor $13$ out of $- 78$ .

$\frac{13 y + 13 \cdot - 6}{2} = 0$

Factor $13$ out of $13 y + 13 \cdot - 6$ .

$\frac{13 (y - 6)}{2} = 0$

Multiply both sides of the equation by $\frac{2}{13}$ .

$\frac{2}{13} \cdot \frac{13 (y - 6)}{2} = \frac{2}{13} \cdot 0$

Simplify both sides of the equation.

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Simplify $\frac{2}{13} \cdot \frac{13 (y - 6)}{2}$ .

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Cancel the common factor of $2$ .

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Cancel the common factor.

$\frac{2}{13} \cdot \frac{13 (y - 6)}{2} = \frac{2}{13} \cdot 0$

Rewrite the expression.

$\frac{1}{13} \cdot (13 (y - 6)) = \frac{2}{13} \cdot 0$

Cancel the common factor of $13$ .

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Cancel the common factor.

$\frac{1}{13} \cdot (13 (y - 6)) = \frac{2}{13} \cdot 0$

Rewrite the expression.

$y - 6 = \frac{2}{13} \cdot 0$

Multiply $\frac{2}{13}$ by $0$ .

$y - 6 = 0$

Add $6$ to both sides of the equation.

$y = 6$

Solve for y (9y+4)/3=(5y-4)/6+15

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