Solve 3(x+2)(x-2)=(x-4)(x-4)+8x

$$3(x+2)(x-2)=(x-4)(x-4)+8x$$

Solve for x

$$x=\sqrt{14}\approx 3.741657387$$

$$x=-\sqrt{14}\approx -3.741657387$$

Steps by Finding Square Root

Multiply x-4 and x-4 to get \left(x-4\right)^{2}.

$$3\left(x+2\right)\left(x-2\right)=\left(x-4\right)^{2}+8x$$

Use the distributive property to multiply 3 by x+2.

$$\left(3x+6\right)\left(x-2\right)=\left(x-4\right)^{2}+8x$$

Use the distributive property to multiply 3x+6 by x-2 and combine like terms.

$$3x^{2}-12=\left(x-4\right)^{2}+8x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$3x^{2}-12=x^{2}-8x+16+8x$$

Combine -8x and 8x to get 0.

$$3x^{2}-12=x^{2}+16$$

Subtract x^{2} from both sides.

$$3x^{2}-12-x^{2}=16$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

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

Add 12 to both sides.

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

Add 16 and 12 to get 28.

$$2x^{2}=28$$

Divide both sides by 2.

$$x^{2}=\frac{28}{2}$$

Divide 28 by 2 to get 14.

$$x^{2}=14$$

Take the square root of both sides of the equation.

$$x=\sqrt{14} x=-\sqrt{14}$$

Steps Using the Quadratic Formula

Multiply x-4 and x-4 to get \left(x-4\right)^{2}.

$$3\left(x+2\right)\left(x-2\right)=\left(x-4\right)^{2}+8x$$

Use the distributive property to multiply 3 by x+2.

$$\left(3x+6\right)\left(x-2\right)=\left(x-4\right)^{2}+8x$$

Use the distributive property to multiply 3x+6 by x-2 and combine like terms.

$$3x^{2}-12=\left(x-4\right)^{2}+8x$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-4\right)^{2}.

$$3x^{2}-12=x^{2}-8x+16+8x$$

Combine -8x and 8x to get 0.

$$3x^{2}-12=x^{2}+16$$

Subtract x^{2} from both sides.

$$3x^{2}-12-x^{2}=16$$

Combine 3x^{2} and -x^{2} to get 2x^{2}.

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

Subtract 16 from both sides.

$$2x^{2}-12-16=0$$

Subtract 16 from -12 to get -28.

$$2x^{2}-28=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -28 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-28\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-28\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-28\right)}}{2\times 2}$$

Multiply -8 times -28.

$$x=\frac{0±\sqrt{224}}{2\times 2}$$

Take the square root of 224.

$$x=\frac{0±4\sqrt{14}}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4\sqrt{14}}{4}$$

Now solve the equation x=\frac{0±4\sqrt{14}}{4} when ± is plus.

$$x=\sqrt{14}$$

Now solve the equation x=\frac{0±4\sqrt{14}}{4} when ± is minus.

$$x=-\sqrt{14}$$

The equation is now solved.

$$x=\sqrt{14} x=-\sqrt{14}$$