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

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

Solve for x

$$x=4$$

$$x=0$$

Steps Using Factoring

Use the distributive property to multiply 6x by 2x+2.

$$12x^{2}+12x=2x\left(8x-2\right)$$

Use the distributive property to multiply 2x by 8x-2.

$$12x^{2}+12x=16x^{2}-4x$$

Subtract 16x^{2} from both sides.

$$12x^{2}+12x-16x^{2}=-4x$$

Combine 12x^{2} and -16x^{2} to get -4x^{2}.

$$-4x^{2}+12x=-4x$$

Add 4x to both sides.

$$-4x^{2}+12x+4x=0$$

Combine 12x and 4x to get 16x.

$$-4x^{2}+16x=0$$

Factor out x.

$$x\left(-4x+16\right)=0$$

To find equation solutions, solve x=0 and -4x+16=0.

$$x=0 x=4$$

Steps Using the Quadratic Formula

Use the distributive property to multiply 6x by 2x+2.

$$12x^{2}+12x=2x\left(8x-2\right)$$

Use the distributive property to multiply 2x by 8x-2.

$$12x^{2}+12x=16x^{2}-4x$$

Subtract 16x^{2} from both sides.

$$12x^{2}+12x-16x^{2}=-4x$$

Combine 12x^{2} and -16x^{2} to get -4x^{2}.

$$-4x^{2}+12x=-4x$$

Add 4x to both sides.

$$-4x^{2}+12x+4x=0$$

Combine 12x and 4x to get 16x.

$$-4x^{2}+16x=0$$

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

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

Take the square root of 16^{2}.

$$x=\frac{-16±16}{2\left(-4\right)}$$

Multiply 2 times -4.

$$x=\frac{-16±16}{-8}$$

Now solve the equation x=\frac{-16±16}{-8} when ± is plus. Add -16 to 16.

$$x=\frac{0}{-8}$$

Divide 0 by -8.

$$x=0$$

Now solve the equation x=\frac{-16±16}{-8} when ± is minus. Subtract 16 from -16.

$$x=-\frac{32}{-8}$$

Divide -32 by -8.

$$x=4$$

The equation is now solved.

$$x=0 x=4$$

Steps for Completing the Square

Use the distributive property to multiply 6x by 2x+2.

$$12x^{2}+12x=2x\left(8x-2\right)$$

Use the distributive property to multiply 2x by 8x-2.

$$12x^{2}+12x=16x^{2}-4x$$

Subtract 16x^{2} from both sides.

$$12x^{2}+12x-16x^{2}=-4x$$

Combine 12x^{2} and -16x^{2} to get -4x^{2}.

$$-4x^{2}+12x=-4x$$

Add 4x to both sides.

$$-4x^{2}+12x+4x=0$$

Combine 12x and 4x to get 16x.

$$-4x^{2}+16x=0$$

Divide both sides by -4.

$$\frac{-4x^{2}+16x}{-4}=\frac{0}{-4}$$

Dividing by -4 undoes the multiplication by -4.

$$x^{2}+\frac{16}{-4}x=\frac{0}{-4}$$

Divide 16 by -4.

$$x^{2}-4x=\frac{0}{-4}$$

Divide 0 by -4.

$$x^{2}-4x=0$$

Divide -4, the coefficient of the x term, by 2 to get -2. Then add the square of -2 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

$$x^{2}-4x+\left(-2\right)^{2}=\left(-2\right)^{2}$$

Square -2.

$$x^{2}-4x+4=4$$

Factor x^{2}-4x+4. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(x-2\right)^{2}=4$$

Take the square root of both sides of the equation.

$$\sqrt{\left(x-2\right)^{2}}=\sqrt{4}$$

Simplify.

$$x-2=2 x-2=-2$$

Add 2 to both sides of the equation.

$$x=4 x=0$$