Solve for x x^2-6x=x(8+x)

$x^{2} - 6 x = x (8 + x)$

Step 1

Simplify $x (8 + x)$ .

Apply the distributive property.

$x^{2} - 6 x = x \cdot 8 + x \cdot x$

Simplify the expression.

Move $8$ to the left of $x$ .

$x^{2} - 6 x = 8 \cdot x + x \cdot x$

Multiply $x$ by $x$ .

$x^{2} - 6 x = 8 x + x^{2}$

Step 2

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

Subtract $8 x$ from both sides of the equation.

$x^{2} - 6 x - 8 x = x^{2}$

Subtract $x^{2}$ from both sides of the equation.

$x^{2} - 6 x - 8 x - x^{2} = 0$

Combine the opposite terms in $x^{2} - 6 x - 8 x - x^{2}$ .

Subtract $x^{2}$ from $x^{2}$ .

$- 6 x - 8 x + 0 = 0$

Add $- 6 x - 8 x$ and $0$ .

$- 6 x - 8 x = 0$

Subtract $8 x$ from $- 6 x$ .

$- 14 x = 0$

Step 3

Divide each term in $- 14 x = 0$ by $- 14$ and simplify.

Divide each term in $- 14 x = 0$ by $- 14$ .

$\frac{- 14 x}{- 14} = \frac{0}{- 14}$

Simplify the left side.

Cancel the common factor of $- 14$ .

Cancel the common factor.

$\frac{- 14 x}{- 14} = \frac{0}{- 14}$

Divide $x$ by $1$ .

$x = \frac{0}{- 14}$

Simplify the right side.

Divide $0$ by $- 14$ .

$x = 0$