Solve (2x+3)(x-1)+3x+3=0

$$( 2 x + 3 ) ( x - 1 ) + 3 x + 3 = 0$$

Solve for x

$$x=-2$$

$$x=0$$

Steps Using Factoring

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

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

Combine x and 3x to get 4x.

$$2x^{2}+4x-3+3=0$$

Add -3 and 3 to get 0.

$$2x^{2}+4x=0$$

Factor out x.

$$x\left(2x+4\right)=0$$

To find equation solutions, solve x=0 and 2x+4=0.

$$x=0 x=-2$$

Steps Using the Quadratic Formula

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

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

Combine x and 3x to get 4x.

$$2x^{2}+4x-3+3=0$$

Add -3 and 3 to get 0.

$$2x^{2}+4x=0$$

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

$$x=\frac{-4±\sqrt{4^{2}}}{2\times 2}$$

Take the square root of 4^{2}.

$$x=\frac{-4±4}{2\times 2}$$

Multiply 2 times 2.

$$x=\frac{-4±4}{4}$$

Now solve the equation x=\frac{-4±4}{4} when ± is plus. Add -4 to 4.

$$x=\frac{0}{4}$$

Divide 0 by 4.

$$x=0$$

Now solve the equation x=\frac{-4±4}{4} when ± is minus. Subtract 4 from -4.

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

Divide -8 by 4.

$$x=-2$$

The equation is now solved.

$$x=0 x=-2$$

Steps for Completing the Square

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

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

Combine x and 3x to get 4x.

$$2x^{2}+4x-3+3=0$$

Add -3 and 3 to get 0.

$$2x^{2}+4x=0$$

Divide both sides by 2.

$$\frac{2x^{2}+4x}{2}=\frac{0}{2}$$

Dividing by 2 undoes the multiplication by 2.

$$x^{2}+\frac{4}{2}x=\frac{0}{2}$$

Divide 4 by 2.

$$x^{2}+2x=\frac{0}{2}$$

Divide 0 by 2.

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

Divide 2, the coefficient of the x term, by 2 to get 1. Then add the square of 1 to both sides of the equation. This step makes the left hand side of the equation a perfect square.

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

Square 1.

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

Factor x^{2}+2x+1. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

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

Take the square root of both sides of the equation.

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

Simplify.

$$x+1=1 x+1=-1$$

Subtract 1 from both sides of the equation.

$$x=0 x=-2$$