Solve (x+1)(x-3)+(x+1)^2=2x(x-4)

$$( x + 1 ) ( x - 3 ) + ( x + 1 ) ^ { 2 } = 2 x ( x - 4 )$$

Solve for x

$$x=\frac{1}{4}=0.25$$

Steps for Solving Linear Equation

Use the distributive property to multiply x+1 by x-3 and combine like terms.

$$x^{2}-2x-3+\left(x+1\right)^{2}=2x\left(x-4\right)$$

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

$$x^{2}-2x-3+x^{2}+2x+1=2x\left(x-4\right)$$

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

$$2x^{2}-2x-3+2x+1=2x\left(x-4\right)$$

Combine -2x and 2x to get 0.

$$2x^{2}-3+1=2x\left(x-4\right)$$

Add -3 and 1 to get -2.

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

Use the distributive property to multiply 2x by x-4.

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

Subtract 2x^{2} from both sides.

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

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

$$-2=-8x$$

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

$$-8x=-2$$

Divide both sides by -8.

$$x=\frac{-2}{-8}$$

Reduce the fraction \frac{-2}{-8} to lowest terms by extracting and canceling out -2.

$$x=\frac{1}{4}$$