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

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

Solve for x

$$x = -\frac{3}{2} = -1\frac{1}{2} = -1.5$$

Steps for Solving Linear Equation

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

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

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

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

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

$$1-2x+x^{2}-x^{2}+2x-1=2x+3$$

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

$$1-2x+2x-1=2x+3$$

Combine -2x and 2x to get 0.

$$1-1=2x+3$$

Subtract 1 from 1 to get 0.

$$0=2x+3$$

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

$$2x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$2x=-3$$

Divide both sides by 2.

$$x=\frac{-3}{2}$$

Fraction \frac{-3}{2} can be rewritten as -\frac{3}{2} by extracting the negative sign.

$$x=-\frac{3}{2}$$