Solve 2left(x+1right)^2-left(x-2right)^2=xleft(x-3right)

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

Solve for x

$$x=\frac{2}{11}\approx 0.181818182$$

Steps for Solving Linear Equation

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

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

Use the distributive property to multiply 2 by x^{2}+2x+1.

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

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

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

To find the opposite of x^{2}-4x+4, find the opposite of each term.

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

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

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

Combine 4x and 4x to get 8x.

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

Subtract 4 from 2 to get -2.

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

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

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

Subtract x^{2} from both sides.

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

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

$$8x-2=-3x$$

Add 3x to both sides.

$$8x-2+3x=0$$

Combine 8x and 3x to get 11x.

$$11x-2=0$$

Add 2 to both sides. Anything plus zero gives itself.

$$11x=2$$

Divide both sides by 11.

$$x=\frac{2}{11}$$