Solve for a y=-n^3+3/4a

$y = - n^{3} + \frac{3}{4} a$

Step 1

Rewrite the equation as $- n^{3} + \frac{3}{4} a = y$ .

$- n^{3} + \frac{3}{4} a = y$

Step 2

Combine $\frac{3}{4}$ and $a$ .

$- n^{3} + \frac{3 a}{4} = y$

Step 3

Add $n^{3}$ to both sides of the equation.

$\frac{3 a}{4} = y + n^{3}$

Step 4

Multiply both sides of the equation by $\frac{4}{3}$ .

$\frac{4}{3} \cdot \frac{3 a}{4} = \frac{4}{3} (y + n^{3})$

Step 5

Simplify both sides of the equation.

Simplify the left side.

Simplify $\frac{4}{3} \cdot \frac{3 a}{4}$ .

Cancel the common factor of $4$ .

Cancel the common factor.

$\frac{4}{3} \cdot \frac{3 a}{4} = \frac{4}{3} (y + n^{3})$

Rewrite the expression.

$\frac{1}{3} (3 a) = \frac{4}{3} (y + n^{3})$

Cancel the common factor of $3$ .

Factor $3$ out of $3 a$ .

$\frac{1}{3} (3 (a)) = \frac{4}{3} (y + n^{3})$

Cancel the common factor.

$\frac{1}{3} (3 a) = \frac{4}{3} (y + n^{3})$

Rewrite the expression.

$a = \frac{4}{3} (y + n^{3})$

Simplify the right side.

Simplify $\frac{4}{3} (y + n^{3})$ .

Apply the distributive property.

$a = \frac{4}{3} y + \frac{4}{3} n^{3}$

Combine $\frac{4}{3}$ and $y$ .

$a = \frac{4 y}{3} + \frac{4}{3} n^{3}$

Combine $\frac{4}{3}$ and $n^{3}$ .

$a = \frac{4 y}{3} + \frac{4 n^{3}}{3}$

Step 6

Reorder $\frac{4 y}{3}$ and $\frac{4 n^{3}}{3}$ .

$a = \frac{4 n^{3}}{3} + \frac{4 y}{3}$