Solve left(x+1right)^3-left(x-1right)^3=6x(x-3)

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

Solve for x

$$x=-\frac{1}{9}\approx -0.111111111$$

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+1\right)^{3}.

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

Use binomial theorem \left(a-b\right)^{3}=a^{3}-3a^{2}b+3ab^{2}-b^{3} to expand \left(x-1\right)^{3}.

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

To find the opposite of x^{3}-3x^{2}+3x-1, find the opposite of each term.

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

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

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

Combine 3x^{2} and 3x^{2} to get 6x^{2}.

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

Combine 3x and -3x to get 0.

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

Add 1 and 1 to get 2.

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

Use the distributive property to multiply 6x by x-3.

$$6x^{2}+2=6x^{2}-18x$$

Subtract 6x^{2} from both sides.

$$6x^{2}+2-6x^{2}=-18x$$

Combine 6x^{2} and -6x^{2} to get 0.

$$2=-18x$$

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

$$-18x=2$$

Divide both sides by -18.

$$x=\frac{2}{-18}$$

Reduce the fraction \frac{2}{-18} to lowest terms by extracting and canceling out 2.

$$x=-\frac{1}{9}$$