Solve (y+2)(y-4)=27

$$( y + 2 ) ( y - 4 ) = 27$$

Solve for y

$$y=-5$$

$$y=7$$

Steps Using the Quadratic Formula

Use the distributive property to multiply y+2 by y-4 and combine like terms.

$$y^{2}-2y-8=27$$

Subtract 27 from both sides.

$$y^{2}-2y-8-27=0$$

Subtract 27 from -8 to get -35.

$$y^{2}-2y-35=0$$

This equation is in standard form: ax^{2}+bx+c=0. Substitute 1 for a, -2 for b, and -35 for c in the quadratic formula, \frac{-b±\sqrt{b^{2}-4ac}}{2a}.

$$y=\frac{-\left(-2\right)±\sqrt{\left(-2\right)^{2}-4\left(-35\right)}}{2}$$

Square -2.

$$y=\frac{-\left(-2\right)±\sqrt{4-4\left(-35\right)}}{2}$$

Multiply -4 times -35.

$$y=\frac{-\left(-2\right)±\sqrt{4+140}}{2}$$

Add 4 to 140.

$$y=\frac{-\left(-2\right)±\sqrt{144}}{2}$$

Take the square root of 144.

$$y=\frac{-\left(-2\right)±12}{2}$$

The opposite of -2 is 2.

$$y=\frac{2±12}{2}$$

Now solve the equation y=\frac{2±12}{2} when ± is plus. Add 2 to 12.

$$y=\frac{14}{2}$$

Divide 14 by 2.

$$y=7$$

Now solve the equation y=\frac{2±12}{2} when ± is minus. Subtract 12 from 2.

$$y=-\frac{10}{2}$$

Divide -10 by 2.

$$y=-5$$

The equation is now solved.

$$y=7 y=-5$$

Steps for Completing the Square

Use the distributive property to multiply y+2 by y-4 and combine like terms.

$$y^{2}-2y-8=27$$

Add 8 to both sides.

$$y^{2}-2y=27+8$$

Add 27 and 8 to get 35.

$$y^{2}-2y=35$$

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.

$$y^{2}-2y+1=35+1$$

Add 35 to 1.

$$y^{2}-2y+1=36$$

Factor y^{2}-2y+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}.

$$\left(y-1\right)^{2}=36$$

Take the square root of both sides of the equation.

$$\sqrt{\left(y-1\right)^{2}}=\sqrt{36}$$

Simplify.

$$y-1=6 y-1=-6$$

Add 1 to both sides of the equation.

$$y=7 y=-5$$