Solve (x+2)^3-(x-2)^3=12x*(x-1)-8

$$( x + 2 ) ^ { 3 } - ( x - 2 ) ^ { 3 } = 12 x \cdot ( x - 1 ) - 8$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a+b\right)^{3}=a^{3}+3a^{2}b+3ab^{2}+b^{3} to expand \left(x+2\right)^{3}.

$$x^{3}+6x^{2}+12x+8-\left(x-2\right)^{3}=12x\left(x-1\right)-8$$

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-2\right)^{3}.

$$x^{3}+6x^{2}+12x+8-\left(x^{3}-6x^{2}+12x-8\right)=12x\left(x-1\right)-8$$

To find the opposite of x^{3}-6x^{2}+12x-8, find the opposite of each term.

$$x^{3}+6x^{2}+12x+8-x^{3}+6x^{2}-12x+8=12x\left(x-1\right)-8$$

Combine x^{3} and -x^{3} to get 0.

$$6x^{2}+12x+8+6x^{2}-12x+8=12x\left(x-1\right)-8$$

Combine 6x^{2} and 6x^{2} to get 12x^{2}.

$$12x^{2}+12x+8-12x+8=12x\left(x-1\right)-8$$

Combine 12x and -12x to get 0.

$$12x^{2}+8+8=12x\left(x-1\right)-8$$

Add 8 and 8 to get 16.

$$12x^{2}+16=12x\left(x-1\right)-8$$

Use the distributive property to multiply 12x by x-1.

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

Subtract 12x^{2} from both sides.

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

Combine 12x^{2} and -12x^{2} to get 0.

$$16=-12x-8$$

Swap sides so that all variable terms are on the left hand side.

$$-12x-8=16$$

Add 8 to both sides.

$$-12x=16+8$$

Add 16 and 8 to get 24.

$$-12x=24$$

Divide both sides by -12.

$$x=\frac{24}{-12}$$

Divide 24 by -12 to get -2.

$$x=-2$$