Solve for a 2-3a^3=-148

$2 - 3 a^{3} = - 148$

Move all terms not containing $a$ to the right side of the equation.

Subtract $2$ from both sides of the equation.

$- 3 a^{3} = - 148 - 2$

Subtract $2$ from $- 148$ .

$- 3 a^{3} = - 150$

Add $150$ to both sides of the equation.

$- 3 a^{3} + 150 = 0$

Factor $- 3$ out of $- 3 a^{3} + 150$ .

Factor $- 3$ out of $150$ .

$- 3 a^{3} - 3 \cdot - 50 = 0$

Factor $- 3$ out of $- 3 (a^{3}) - 3 (- 50)$ .

$- 3 (a^{3} - 50) = 0$

Divide each term in $- 3 (a^{3} - 50) = 0$ by $- 3$ and simplify.

Divide each term in $- 3 (a^{3} - 50) = 0$ by $- 3$ .

$\frac{- 3 (a^{3} - 50)}{- 3} = \frac{0}{- 3}$

Simplify the left side.

Cancel the common factor of $- 3$ .

Cancel the common factor.

$\frac{- 3 (a^{3} - 50)}{- 3} = \frac{0}{- 3}$

Divide $a^{3} - 50$ by $1$ .

$a^{3} - 50 = \frac{0}{- 3}$

Simplify the right side.

Divide $0$ by $- 3$ .

$a^{3} - 50 = 0$

Add $50$ to both sides of the equation.

$a^{3} = 50$

Take the cube root of both sides of the equation to eliminate the exponent on the left side.

$a = \sqrt[3]{50}$

The result can be shown in multiple forms.

Exact Form:

$a = \sqrt[3]{50}$

Decimal Form:

$a = 3.68403149 \dots$