Solve left(x-1right)left(2x+3right)=x-1

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

Solve for x

$$x=-1$$

$$x=1$$

Steps by Finding Square Root

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

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

Add 3 to both sides.

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

Add -1 and 3 to get 2.

$$2x^{2}=2$$

Divide both sides by 2.

$$x^{2}=\frac{2}{2}$$

Divide 2 by 2 to get 1.

$$x^{2}=1$$

Take the square root of both sides of the equation.

$$x=1 x=-1$$

Steps Using the Quadratic Formula

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

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

Subtract x from both sides.

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

Combine x and -x to get 0.

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

Add 1 to both sides.

$$2x^{2}-3+1=0$$

Add -3 and 1 to get -2.

$$2x^{2}-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 2 for a, 0 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$x=\frac{0±\sqrt{0^{2}-4\times 2\left(-2\right)}}{2\times 2}$$

Square 0.

$$x=\frac{0±\sqrt{-4\times 2\left(-2\right)}}{2\times 2}$$

Multiply -4 times 2.

$$x=\frac{0±\sqrt{-8\left(-2\right)}}{2\times 2}$$

Multiply -8 times -2.

$$x=\frac{0±\sqrt{16}}{2\times 2}$$

Take the square root of 16.

$$x=\frac{0±4}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{0±4}{4}$$

Now solve the equation x=\frac{0±4}{4} when ± is plus. Divide 4 by 4.

$$x=1$$

Now solve the equation x=\frac{0±4}{4} when ± is minus. Divide -4 by 4.

$$x=-1$$

The equation is now solved.

$$x=1 x=-1$$