Solve for f 3M+1/2tf=g^3

$3 M + \frac{1}{2} t f = g^{3}$

Multiply $\frac{1}{2} (t f)$ .

Combine $t$ and $\frac{1}{2}$ .

$3 M + \frac{t}{2} f = g^{3}$

Combine $\frac{t}{2}$ and $f$ .

$3 M + \frac{t f}{2} = g^{3}$

Subtract $3 M$ from both sides of the equation.

$\frac{t f}{2} = g^{3} - 3 M$

Multiply both sides of the equation by $2$ .

$2 \frac{t f}{2} = 2 (g^{3} - 3 M)$

Simplify both sides of the equation.

Simplify the left side.

Cancel the common factor of $2$ .

Cancel the common factor.

$2 \frac{t f}{2} = 2 (g^{3} - 3 M)$

Rewrite the expression.

$t f = 2 (g^{3} - 3 M)$

Simplify the right side.

Simplify $2 (g^{3} - 3 M)$ .

Apply the distributive property.

$t f = 2 g^{3} + 2 (- 3 M)$

Multiply $- 3$ by $2$ .

$t f = 2 g^{3} - 6 M$

Divide each term in $t f = 2 g^{3} - 6 M$ by $t$ and simplify.

Divide each term in $t f = 2 g^{3} - 6 M$ by $t$ .

$\frac{t f}{t} = \frac{2 g^{3}}{t} + \frac{- 6 M}{t}$

Simplify the left side.

Cancel the common factor of $t$ .

Cancel the common factor.

$\frac{t f}{t} = \frac{2 g^{3}}{t} + \frac{- 6 M}{t}$

Divide $f$ by $1$ .

$f = \frac{2 g^{3}}{t} + \frac{- 6 M}{t}$

Simplify the right side.

Move the negative in front of the fraction.

$f = \frac{2 g^{3}}{t} - \frac{6 M}{t}$