Solve for x x(x^2-1)=3+x^3

$x (x^{2} - 1) = 3 + x^{3}$

Step 1

Simplify $x (x^{2} - 1)$ .

Rewrite.

$0 + 0 + x (x^{2} - 1) = 3 + x^{3}$

Simplify by adding zeros.

$x (x^{2} - 1) = 3 + x^{3}$

Apply the distributive property.

$x \cdot x^{2} + x \cdot - 1 = 3 + x^{3}$

Multiply $x$ by $x^{2}$ by adding the exponents.

Multiply $x$ by $x^{2}$ .

Raise $x$ to the power of $1$ .

$x^{1} x^{2} + x \cdot - 1 = 3 + x^{3}$

Use the power rule $a^{m} a^{n} = a^{m + n}$ to combine exponents.

$x^{1 + 2} + x \cdot - 1 = 3 + x^{3}$

Add $1$ and $2$ .

$x^{3} + x \cdot - 1 = 3 + x^{3}$

Move $- 1$ to the left of $x$ .

$x^{3} - 1 \cdot x = 3 + x^{3}$

Rewrite $- 1 x$ as $- x$ .

$x^{3} - x = 3 + x^{3}$

Step 2

Move all terms containing $x$ to the left side of the equation.

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

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

Combine the opposite terms in $x^{3} - x - x^{3}$ .

Subtract $x^{3}$ from $x^{3}$ .

$- x + 0 = 3$

Add $- x$ and $0$ .

$- x = 3$

Step 3

Divide each term in $- x = 3$ by $- 1$ and simplify.

Divide each term in $- x = 3$ by $- 1$ .

$\frac{- x}{- 1} = \frac{3}{- 1}$

Simplify the left side.

Dividing two negative values results in a positive value.

$\frac{x}{1} = \frac{3}{- 1}$

Divide $x$ by $1$ .

$x = \frac{3}{- 1}$

Simplify the right side.

Divide $3$ by $- 1$ .

$x = - 3$