Solve for z z+z+z+y+y=9zy

$z + z + z + y + y = 9 z y$

Simplify $z + z + z + y + y$ .

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Add $z$ and $z$ .

$2 z + z + y + y = 9 z y$

Add $2 z$ and $z$ .

$3 z + y + y = 9 z y$

Add $y$ and $y$ .

$3 z + 2 y = 9 z y$

Subtract $9 z y$ from both sides of the equation.

$3 z + 2 y - 9 z y = 0$

Subtract $2 y$ from both sides of the equation.

$3 z - 9 z y = - 2 y$

Factor $3 z$ out of $3 z - 9 z y$ .

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Factor $3 z$ out of $3 z$ .

$3 z (1) - 9 z y = - 2 y$

Factor $3 z$ out of $- 9 z y$ .

$3 z (1) + 3 z (- 3 y) = - 2 y$

Factor $3 z$ out of $3 z (1) + 3 z (- 3 y)$ .

$3 z (1 - 3 y) = - 2 y$

Divide each term by $3 (1 - 3 y)$ and simplify.

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Divide each term in $3 z (1 - 3 y) = - 2 y$ by $3 (1 - 3 y)$ .

$\frac{3 z (1 - 3 y)}{3 (1 - 3 y)} = \frac{- 2 y}{3 (1 - 3 y)}$

Simplify $\frac{3 z (1 - 3 y)}{3 (1 - 3 y)}$ .

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Cancel the common factor of $3$ .

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Cancel the common factor.

$\frac{3 z (1 - 3 y)}{3 (1 - 3 y)} = \frac{- 2 y}{3 (1 - 3 y)}$

Rewrite the expression.

$\frac{z (1 - 3 y)}{1 - 3 y} = \frac{- 2 y}{3 (1 - 3 y)}$

Cancel the common factor of $1 - 3 y$ .

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Cancel the common factor.

$\frac{z (1 - 3 y)}{1 - 3 y} = \frac{- 2 y}{3 (1 - 3 y)}$

Divide $z$ by $1$ .

$z = \frac{- 2 y}{3 (1 - 3 y)}$

Move the negative in front of the fraction.

$z = - \frac{2 y}{3 (1 - 3 y)}$

Solve for z z+z+z+y+y=9zy

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