Solve (5x-2)^2=(25x+2)(x-1)

$$( 5 x - 2 ) ^ { 2 } = ( 25 x + 2 ) ( x - 1 )$$

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(5x-2\right)^{2}.

$$25x^{2}-20x+4=\left(25x+2\right)\left(x-1\right)$$

Use the distributive property to multiply 25x+2 by x-1 and combine like terms.

$$25x^{2}-20x+4=25x^{2}-23x-2$$

Subtract 25x^{2} from both sides.

$$25x^{2}-20x+4-25x^{2}=-23x-2$$

Combine 25x^{2} and -25x^{2} to get 0.

$$-20x+4=-23x-2$$

Add 23x to both sides.

$$-20x+4+23x=-2$$

Combine -20x and 23x to get 3x.

$$3x+4=-2$$

Subtract 4 from both sides.

$$3x=-2-4$$

Subtract 4 from -2 to get -6.

$$3x=-6$$

Divide both sides by 3.

$$x=\frac{-6}{3}$$

Divide -6 by 3 to get -2.

$$x=-2$$