Solve for A 3q^3=-8+D/A

$3 q^{3} = - 8 + \frac{D}{A}$

Rewrite the equation as $- 8 + \frac{D}{A} = 3 q^{3}$ .

$- 8 + \frac{D}{A} = 3 q^{3}$

Add $8$ to both sides of the equation.

$\frac{D}{A} = 3 q^{3} + 8$

Find the LCD of the terms in the equation.

Finding the LCD of a list of values is the same as finding the LCM of the denominators of those values.

$A, 1, 1$

The LCM of one and any expression is the expression.

$A$

Multiply each term in $\frac{D}{A} = 3 q^{3} + 8$ by $A$ to eliminate the fractions.

Multiply each term in $\frac{D}{A} = 3 q^{3} + 8$ by $A$ .

$\frac{D}{A} A = 3 q^{3} A + 8 A$

Simplify the left side.

Cancel the common factor of $A$ .

Cancel the common factor.

$\frac{D}{A} A = 3 q^{3} A + 8 A$

Rewrite the expression.

$D = 3 q^{3} A + 8 A$

Solve the equation.

Rewrite the equation as $3 q^{3} A + 8 A = D$ .

$3 q^{3} A + 8 A = D$

Factor $A$ out of $3 q^{3} A + 8 A$ .

Factor $A$ out of $3 q^{3} A$ .

$A (3 q^{3}) + 8 A = D$

Factor $A$ out of $8 A$ .

$A (3 q^{3}) + A \cdot 8 = D$

Factor $A$ out of $A (3 q^{3}) + A \cdot 8$ .

$A (3 q^{3} + 8) = D$

Divide each term in $A (3 q^{3} + 8) = D$ by $3 q^{3} + 8$ and simplify.

Divide each term in $A (3 q^{3} + 8) = D$ by $3 q^{3} + 8$ .

$\frac{A (3 q^{3} + 8)}{3 q^{3} + 8} = \frac{D}{3 q^{3} + 8}$

Simplify the left side.

Cancel the common factor of $3 q^{3} + 8$ .

Cancel the common factor.

$\frac{A (3 q^{3} + 8)}{3 q^{3} + 8} = \frac{D}{3 q^{3} + 8}$

Divide $A$ by $1$ .

$A = \frac{D}{3 q^{3} + 8}$