Solve for A 8x^3=(-2x)(A)

$8 x^{3} = (- 2 x) (A)$

Rewrite the equation as $- 2 x A = 8 x^{3}$ .

$- 2 x A = 8 x^{3}$

Divide each term in $- 2 x A = 8 x^{3}$ by $- 2 x$ and simplify.

Divide each term in $- 2 x A = 8 x^{3}$ by $- 2 x$ .

$\frac{- 2 x A}{- 2 x} = \frac{8 x^{3}}{- 2 x}$

Simplify the left side.

Cancel the common factor of $- 2$ .

Cancel the common factor.

$\frac{- 2 x A}{- 2 x} = \frac{8 x^{3}}{- 2 x}$

Rewrite the expression.

$\frac{x A}{x} = \frac{8 x^{3}}{- 2 x}$

Cancel the common factor of $x$ .

Cancel the common factor.

$\frac{x A}{x} = \frac{8 x^{3}}{- 2 x}$

Divide $A$ by $1$ .

$A = \frac{8 x^{3}}{- 2 x}$

Simplify the right side.

Cancel the common factor of $8$ and $- 2$ .

Factor $2$ out of $8 x^{3}$ .

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

Cancel the common factors.

Factor $2$ out of $- 2 x$ .

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

Cancel the common factor.

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

Rewrite the expression.

$A = \frac{4 x^{3}}{- x}$

Cancel the common factor of $x^{3}$ and $x$ .

Factor $x$ out of $4 x^{3}$ .

$A = \frac{x (4 x^{2})}{- x}$

Move the negative one from the denominator of $\frac{4 x^{2}}{- 1}$ .

$A = - 1 \cdot (4 x^{2})$

Simplify the expression.

Rewrite $- 1 \cdot (4 x^{2})$ as $- (4 x^{2})$ .

$A = - (4 x^{2})$

Multiply $4$ by $- 1$ .

$A = - 4 x^{2}$