Solve left(x+3right)^2-2x+1=(x-3)(x+5)+3

$${ \left(x+3 \right) }^{ 2 } -2x+1=(x-3)(x+5)+3$$

Solve for x

$$x=-11$$

Steps for Solving Linear Equation

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

$$x^{2}+6x+9-2x+1=\left(x-3\right)\left(x+5\right)+3$$

Combine 6x and -2x to get 4x.

$$x^{2}+4x+9+1=\left(x-3\right)\left(x+5\right)+3$$

Add 9 and 1 to get 10.

$$x^{2}+4x+10=\left(x-3\right)\left(x+5\right)+3$$

Use the distributive property to multiply x-3 by x+5 and combine like terms.

$$x^{2}+4x+10=x^{2}+2x-15+3$$

Add -15 and 3 to get -12.

$$x^{2}+4x+10=x^{2}+2x-12$$

Subtract x^{2} from both sides.

$$x^{2}+4x+10-x^{2}=2x-12$$

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

$$4x+10=2x-12$$

Subtract 2x from both sides.

$$4x+10-2x=-12$$

Combine 4x and -2x to get 2x.

$$2x+10=-12$$

Subtract 10 from both sides.

$$2x=-12-10$$

Subtract 10 from -12 to get -22.

$$2x=-22$$

Divide both sides by 2.

$$x=\frac{-22}{2}$$

Divide -22 by 2 to get -11.

$$x=-11$$