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

$$( x - 2 ) ( x + 8 ) = 6 x$$

Solve for x

$$x=-4$$

$$x=4$$

Steps Using Difference of Squares

Use the distributive property to multiply x-2 by x+8 and combine like terms.

$$x^{2}+6x-16=6x$$

Subtract 6x from both sides.

$$x^{2}+6x-16-6x=0$$

Combine 6x and -6x to get 0.

$$x^{2}-16=0$$

Consider x^{2}-16. Rewrite x^{2}-16 as x^{2}-4^{2}. The difference of squares can be factored using the rule: a^{2}-b^{2}=\left(a-b\right)\left(a+b\right).

$$\left(x-4\right)\left(x+4\right)=0$$

To find equation solutions, solve x-4=0 and x+4=0.

$$x=4 x=-4$$

Steps by Finding Square Root

Use the distributive property to multiply x-2 by x+8 and combine like terms.

$$x^{2}+6x-16=6x$$

Subtract 6x from both sides.

$$x^{2}+6x-16-6x=0$$

Combine 6x and -6x to get 0.

$$x^{2}-16=0$$

Add 16 to both sides. Anything plus zero gives itself.

$$x^{2}=16$$

Take the square root of both sides of the equation.

$$x=4 x=-4$$

Steps Using the Quadratic Formula

Use the distributive property to multiply x-2 by x+8 and combine like terms.

$$x^{2}+6x-16=6x$$

Subtract 6x from both sides.

$$x^{2}+6x-16-6x=0$$

Combine 6x and -6x to get 0.

$$x^{2}-16=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 0 for b, and -16 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\left(-16\right)}}{2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\left(-16\right)}}{2}$$

Multiply -4 times -16.

$$x=\frac{0±\sqrt{64}}{2}$$

Take the square root of 64.

$$x=\frac{0±8}{2}$$

Now solve the equation x=\frac{0±8}{2} when ± is plus. Divide 8 by 2.

$$x=4$$

Now solve the equation x=\frac{0±8}{2} when ± is minus. Divide -8 by 2.

$$x=-4$$

The equation is now solved.

$$x=4 x=-4$$