Solve (x-7)^2=(2x-3)^2-3x^2

$$( x - 7 ) ^ { 2 } = ( 2 x - 3 ) ^ { 2 } - 3 x ^ { 2 }$$

Solve for x

$$x=20$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(x-7\right)^{2}.

$$x^{2}-14x+49=\left(2x-3\right)^{2}-3x^{2}$$

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

$$x^{2}-14x+49=4x^{2}-12x+9-3x^{2}$$

Combine 4x^{2} and -3x^{2} to get x^{2}.

$$x^{2}-14x+49=x^{2}-12x+9$$

Subtract x^{2} from both sides.

$$x^{2}-14x+49-x^{2}=-12x+9$$

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

$$-14x+49=-12x+9$$

Add 12x to both sides.

$$-14x+49+12x=9$$

Combine -14x and 12x to get -2x.

$$-2x+49=9$$

Subtract 49 from both sides.

$$-2x=9-49$$

Subtract 49 from 9 to get -40.

$$-2x=-40$$

Divide both sides by -2.

$$x=\frac{-40}{-2}$$

Divide -40 by -2 to get 20.

$$x=20$$