Solve for x
x=2
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x^{2}+2x-3=5+\left(x-2\right)^{2}
Use the distributive property to multiply x+3 by x-1 and combine like terms.
x^{2}+2x-3=5+x^{2}-4x+4
Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-2\right)^{2}.
x^{2}+2x-3=9+x^{2}-4x
Add 5 and 4 to get 9.
x^{2}+2x-3-x^{2}=9-4x
Subtract x^{2} from both sides.
2x-3=9-4x
Combine x^{2} and -x^{2} to get 0.
2x-3+4x=9
Add 4x to both sides.
6x-3=9
Combine 2x and 4x to get 6x.
6x=9+3
Add 3 to both sides.
6x=12
Add 9 and 3 to get 12.
x=\frac{12}{6}
Divide both sides by 6.
x=2
Divide 12 by 6 to get 2.
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