Solve for y x=1/3yz^2+4

$x = \frac{1}{3} y z^{2} + 4$

Rewrite the equation as $\frac{1}{3} \cdot (y z^{2}) + 4 = x$ .

$\frac{1}{3} \cdot (y z^{2}) + 4 = x$

Multiply $\frac{1}{3} (y z^{2})$ .

Combine $y$ and $\frac{1}{3}$ .

$\frac{y}{3} z^{2} + 4 = x$

Combine $\frac{y}{3}$ and $z^{2}$ .

$\frac{y z^{2}}{3} + 4 = x$

Subtract $4$ from both sides of the equation.

$\frac{y z^{2}}{3} = x - 4$

Multiply both sides of the equation by $3$ .

$3 \frac{y z^{2}}{3} = 3 (x - 4)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

$3 \frac{y z^{2}}{3} = 3 (x - 4)$

Rewrite the expression.

$y z^{2} = 3 (x - 4)$

Simplify the right side.

Simplify $3 (x - 4)$ .

Apply the distributive property.

$y z^{2} = 3 x + 3 \cdot - 4$

Multiply $3$ by $- 4$ .

$y z^{2} = 3 x - 12$

Divide each term in $y z^{2} = 3 x - 12$ by $z^{2}$ and simplify.

Divide each term in $y z^{2} = 3 x - 12$ by $z^{2}$ .

$\frac{y z^{2}}{z^{2}} = \frac{3 x}{z^{2}} + \frac{- 12}{z^{2}}$

Simplify the left side.

Cancel the common factor of $z^{2}$ .

Cancel the common factor.

$\frac{y z^{2}}{z^{2}} = \frac{3 x}{z^{2}} + \frac{- 12}{z^{2}}$

Divide $y$ by $1$ .

$y = \frac{3 x}{z^{2}} + \frac{- 12}{z^{2}}$

Simplify the right side.

Move the negative in front of the fraction.

$y = \frac{3 x}{z^{2}} - \frac{12}{z^{2}}$