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

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

Solve for x

$$x=2$$

Steps for Solving Linear Equation

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

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

Combine 2x^{2} and x^{2} to get 3x^{2}.

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

Use the distributive property to multiply 3 by x-1.

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

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

$$3x^{2}-x-1=3x^{2}+3x-6-3$$

Subtract 3 from -6 to get -9.

$$3x^{2}-x-1=3x^{2}+3x-9$$

Subtract 3x^{2} from both sides.

$$3x^{2}-x-1-3x^{2}=3x-9$$

Combine 3x^{2} and -3x^{2} to get 0.

$$-x-1=3x-9$$

Subtract 3x from both sides.

$$-x-1-3x=-9$$

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

$$-4x-1=-9$$

Add 1 to both sides.

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

Add -9 and 1 to get -8.

$$-4x=-8$$

Divide both sides by -4.

$$x=\frac{-8}{-4}$$

Divide -8 by -4 to get 2.

$$x=2$$