Solve (6-2x)^2+9=(3+2x)^2

$$( 6 - 2 x ) ^ { 2 } + 9 = ( 3 + 2 x ) ^ { 2 }$$

Solve for x

$$x=1$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(6-2x\right)^{2}.

$$36-24x+4x^{2}+9=\left(3+2x\right)^{2}$$

Add 36 and 9 to get 45.

$$45-24x+4x^{2}=\left(3+2x\right)^{2}$$

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

$$45-24x+4x^{2}=9+12x+4x^{2}$$

Subtract 12x from both sides.

$$45-24x+4x^{2}-12x=9+4x^{2}$$

Combine -24x and -12x to get -36x.

$$45-36x+4x^{2}=9+4x^{2}$$

Subtract 4x^{2} from both sides.

$$45-36x+4x^{2}-4x^{2}=9$$

Combine 4x^{2} and -4x^{2} to get 0.

$$45-36x=9$$

Subtract 45 from both sides.

$$-36x=9-45$$

Subtract 45 from 9 to get -36.

$$-36x=-36$$

Divide both sides by -36.

$$x=\frac{-36}{-36}$$

Divide -36 by -36 to get 1.

$$x=1$$