Solve (2x-1)^2-(4x-1)(x-2)=0

$$( 2 x - 1 ) ^ { 2 } - ( 4 x - 1 ) ( x - 2 ) = 0$$

Solve for x

$$x=\frac{1}{5}=0.2$$

Steps for Solving Linear Equation

Use binomial theorem \left(a-b\right)^{2}=a^{2}-2ab+b^{2} to expand \left(2x-1\right)^{2}.

$$4x^{2}-4x+1-\left(4x-1\right)\left(x-2\right)=0$$

Use the distributive property to multiply 4x-1 by x-2 and combine like terms.

$$4x^{2}-4x+1-\left(4x^{2}-9x+2\right)=0$$

To find the opposite of 4x^{2}-9x+2, find the opposite of each term.

$$4x^{2}-4x+1-4x^{2}+9x-2=0$$

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

$$-4x+1+9x-2=0$$

Combine -4x and 9x to get 5x.

$$5x+1-2=0$$

Subtract 2 from 1 to get -1.

$$5x-1=0$$

Add 1 to both sides. Anything plus zero gives itself.

$$5x=1$$

Divide both sides by 5.

$$x=\frac{1}{5}$$