Solve 2x+1+(x-2)(2x-1)=2x(x-2)

$$2x+1+(x-2)(2x-1)=2x(x-2)$$

Solve for x

$$x=-3$$

Steps for Solving Linear Equation

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

$$2x+1+2x^{2}-5x+2=2x\left(x-2\right)$$

Combine 2x and -5x to get -3x.

$$-3x+1+2x^{2}+2=2x\left(x-2\right)$$

Add 1 and 2 to get 3.

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

Use the distributive property to multiply 2x by x-2.

$$-3x+3+2x^{2}=2x^{2}-4x$$

Subtract 2x^{2} from both sides.

$$-3x+3+2x^{2}-2x^{2}=-4x$$

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

$$-3x+3=-4x$$

Add 4x to both sides.

$$-3x+3+4x=0$$

Combine -3x and 4x to get x.

$$x+3=0$$

Subtract 3 from both sides. Anything subtracted from zero gives its negation.

$$x=-3$$