Solve (3x-10)^2=(3x-8)^2

$$( 3 x - 10 ) ^ { 2 } = ( 3 x - 8 ) ^ { 2 }$$

Solve for x

$$x=3$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-10\right)^{2}.

$$9x^{2}-60x+100=\left(3x-8\right)^{2}$$

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(3x-8\right)^{2}.

$$9x^{2}-60x+100=9x^{2}-48x+64$$

Subtract 9x^{2} from both sides.

$$9x^{2}-60x+100-9x^{2}=-48x+64$$

Combine 9x^{2} and -9x^{2} to get 0.

$$-60x+100=-48x+64$$

Add 48x to both sides.

$$-60x+100+48x=64$$

Combine -60x and 48x to get -12x.

$$-12x+100=64$$

Subtract 100 from both sides.

$$-12x=64-100$$

Subtract 100 from 64 to get -36.

$$-12x=-36$$

Divide both sides by -12.

$$x=\frac{-36}{-12}$$

Divide -36 by -12 to get 3.

$$x=3$$