Solve for x g(-x)=x^3

$g (- x) = x^{3}$

Step 1

Rewrite using the commutative property of multiplication.

$- g x = x^{3}$

Step 2

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

$- g x - x^{3} = 0$

Step 3

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

Factor $x$ out of $- g x$ .

$x (- g) - x^{3} = 0$

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

$x (- g) + x (- x^{2}) = 0$

Factor $x$ out of $x (- g) + x (- x^{2})$ .

$x (- g - x^{2}) = 0$

Step 4

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$x = 0$

$- g - x^{2} = 0$

Step 5

Set $x$ equal to $0$ .

$x = 0$

Step 6

Set $- g - x^{2}$ equal to $0$ and solve for $x$ .

Set $- g - x^{2}$ equal to $0$ .

$- g - x^{2} = 0$

Solve $- g - x^{2} = 0$ for $x$ .

Add $g$ to both sides of the equation.

$- x^{2} = g$

Divide each term in $- x^{2} = g$ by $- 1$ and simplify.

Divide each term in $- x^{2} = g$ by $- 1$ .

$\frac{- x^{2}}{- 1} = \frac{g}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x^{2}}{1} = \frac{g}{- 1}$

Divide $x^{2}$ by $1$ .

$x^{2} = \frac{g}{- 1}$

Simplify the right side.

Move the negative one from the denominator of $\frac{g}{- 1}$ .

$x^{2} = - 1 \cdot g$

Rewrite $- 1 \cdot g$ as $- g$ .

$x^{2} = - g$

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

$x = \pm \sqrt{- g}$

The complete solution is the result of both the positive and negative portions of the solution.

First, use the positive value of the $\pm$ to find the first solution.

$x = \sqrt{- g}$

Next, use the negative value of the $\pm$ to find the second solution.

$x = - \sqrt{- g}$

The complete solution is the result of both the positive and negative portions of the solution.

$x = \sqrt{- g}$

$x = - \sqrt{- g}$

$x = \sqrt{- g}$

$x = - \sqrt{- g}$

$x = \sqrt{- g}$

$x = - \sqrt{- g}$

$x = \sqrt{- g}$

$x = - \sqrt{- g}$

Step 7

The final solution is all the values that make $x (- g - x^{2}) = 0$ true.

$x = 0$

$x = \sqrt{- g}$

$x = - \sqrt{- g}$

Solve for x g(-x)=x^3

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