Solve for b g^3+(2d)/b=7

$g^{3} + \frac{2 d}{b} = 7$

Subtract $g^{3}$ from both sides of the equation.

$\frac{2 d}{b} = 7 - g^{3}$

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.

$b, 1, 1$

The LCM of one and any expression is the expression.

$b$

Multiply each term in $\frac{2 d}{b} = 7 - g^{3}$ by $b$ to eliminate the fractions.

Multiply each term in $\frac{2 d}{b} = 7 - g^{3}$ by $b$ .

$\frac{2 d}{b} b = 7 b - g^{3} b$

Simplify the left side.

Cancel the common factor of $b$ .

Cancel the common factor.

$\frac{2 d}{b} b = 7 b - g^{3} b$

Rewrite the expression.

$2 d = 7 b - g^{3} b$

Solve the equation.

Rewrite the equation as $7 b - g^{3} b = 2 d$ .

$7 b - g^{3} b = 2 d$

Factor $b$ out of $7 b - g^{3} b$ .

Factor $b$ out of $7 b$ .

$b \cdot 7 - g^{3} b = 2 d$

Factor $b$ out of $- g^{3} b$ .

$b \cdot 7 + b (- g^{3}) = 2 d$

Factor $b$ out of $b \cdot 7 + b (- g^{3})$ .

$b (7 - g^{3}) = 2 d$

Divide each term in $b (7 - g^{3}) = 2 d$ by $7 - g^{3}$ and simplify.

Divide each term in $b (7 - g^{3}) = 2 d$ by $7 - g^{3}$ .

$\frac{b (7 - g^{3})}{7 - g^{3}} = \frac{2 d}{7 - g^{3}}$

Simplify the left side.

Cancel the common factor of $7 - g^{3}$ .

Cancel the common factor.

$\frac{b (7 - g^{3})}{7 - g^{3}} = \frac{2 d}{7 - g^{3}}$

Divide $b$ by $1$ .

$b = \frac{2 d}{7 - g^{3}}$