Solve (y+1)(y+2)=2y+4

$$( y + 1 ) ( y + 2 ) = 2 y + 4$$

Solve for y

$$y=-2$$

$$y=1$$

Steps Using the Quadratic Formula

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

$$y^{2}+3y+2=2y+4$$

Subtract 2y from both sides.

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

Combine 3y and -2y to get y.

$$y^{2}+y+2=4$$

Subtract 4 from both sides.

$$y^{2}+y+2-4=0$$

Subtract 4 from 2 to get -2.

$$y^{2}+y-2=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, 1 for b, and -2 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-1±\sqrt{1^{2}-4\left(-2\right)}}{2}$$

Square 1.

$$y=\frac{-1±\sqrt{1-4\left(-2\right)}}{2}$$

Multiply -4 times -2.

$$y=\frac{-1±\sqrt{1+8}}{2}$$

Add 1 to 8.

$$y=\frac{-1±\sqrt{9}}{2}$$

Take the square root of 9.

$$y=\frac{-1±3}{2}$$

Now solve the equation y=\frac{-1±3}{2} when ± is plus. Add -1 to 3.

$$y=\frac{2}{2}$$

Divide 2 by 2.

$$y=1$$

Now solve the equation y=\frac{-1±3}{2} when ± is minus. Subtract 3 from -1.

$$y=-\frac{4}{2}$$

Divide -4 by 2.

$$y=-2$$

The equation is now solved.

$$y=1 y=-2$$

Steps for Completing the Square

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

$$y^{2}+3y+2=2y+4$$

Subtract 2y from both sides.

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

Combine 3y and -2y to get y.

$$y^{2}+y+2=4$$

Subtract 2 from both sides.

$$y^{2}+y=4-2$$

Subtract 2 from 4 to get 2.

$$y^{2}+y=2$$

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

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

Square \frac{1}{2} by squaring both the numerator and the denominator of the fraction.

$$y^{2}+y+\frac{1}{4}=2+\frac{1}{4}$$

Add 2 to \frac{1}{4}.

$$y^{2}+y+\frac{1}{4}=\frac{9}{4}$$

Factor y^{2}+y+\frac{1}{4}. In general, when x^{2}+bx+c is a perfect square, it can always be factored as \left(x+\frac{b}{2}\right)^{2}.

$$\left(y+\frac{1}{2}\right)^{2}=\frac{9}{4}$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y+\frac{1}{2}\right)^{2}}=\sqrt{\frac{9}{4}}$$

Simplify.

$$y+\frac{1}{2}=\frac{3}{2} y+\frac{1}{2}=-\frac{3}{2}$$

Subtract \frac{1}{2} from both sides of the equation.

$$y=1 y=-2$$