Solve (2x+1)(x-3)-2x=2(x-1)^2+1

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

Solve for x

$$x=-2$$

Steps for Solving Linear Equation

Use the distributive property to multiply 2x+1 by x-3 and combine like terms.

$$2x^{2}-5x-3-2x=2\left(x-1\right)^{2}+1$$

Combine -5x and -2x to get -7x.

$$2x^{2}-7x-3=2\left(x-1\right)^{2}+1$$

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

$$2x^{2}-7x-3=2\left(x^{2}-2x+1\right)+1$$

Use the distributive property to multiply 2 by x^{2}-2x+1.

$$2x^{2}-7x-3=2x^{2}-4x+2+1$$

Add 2 and 1 to get 3.

$$2x^{2}-7x-3=2x^{2}-4x+3$$

Subtract 2x^{2} from both sides.

$$2x^{2}-7x-3-2x^{2}=-4x+3$$

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

$$-7x-3=-4x+3$$

Add 4x to both sides.

$$-7x-3+4x=3$$

Combine -7x and 4x to get -3x.

$$-3x-3=3$$

Add 3 to both sides.

$$-3x=3+3$$

Add 3 and 3 to get 6.

$$-3x=6$$

Divide both sides by -3.

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

Divide 6 by -3 to get -2.

$$x=-2$$