Solve Using the Quadratic Formula (y-3)(y+2)=0

$(y - 3) (y + 2) = 0$

Step 1

Simplify the left side.

Simplify $(y - 3) (y + 2)$ .

Expand $(y - 3) (y + 2)$ using the FOIL Method.

Apply the distributive property.

$y (y + 2) - 3 (y + 2) = 0$

Apply the distributive property.

$y \cdot y + y \cdot 2 - 3 (y + 2) = 0$

Apply the distributive property.

$y \cdot y + y \cdot 2 - 3 y - 3 \cdot 2 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ .

$y^{2} + y \cdot 2 - 3 y - 3 \cdot 2 = 0$

Move $2$ to the left of $y$ .

$y^{2} + 2 \cdot y - 3 y - 3 \cdot 2 = 0$

Multiply $- 3$ by $2$ .

$y^{2} + 2 y - 3 y - 6 = 0$

Subtract $3 y$ from $2 y$ .

$y^{2} - y - 6 = 0$

Step 2

Use the quadratic formula to find the solutions.

$\frac{- b \pm \sqrt{b^{2} - 4 (a c)}}{2 a}$

Step 3

Substitute the values $a = 1$ , $b = - 1$ , and $c = - 6$ into the quadratic formula and solve for $y$ .

$\frac{1 \pm \sqrt{{(- 1)}^{2} - 4 \cdot (1 \cdot - 6)}}{2 \cdot 1}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 1$ to the power of $2$ .

$y = \frac{1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 6}}{2 \cdot 1}$

Multiply $- 4 \cdot 1 \cdot - 6$ .

Multiply $- 4$ by $1$ .

$y = \frac{1 \pm \sqrt{1 - 4 \cdot - 6}}{2 \cdot 1}$

Multiply $- 4$ by $- 6$ .

$y = \frac{1 \pm \sqrt{1 + 24}}{2 \cdot 1}$

Add $1$ and $24$ .

$y = \frac{1 \pm \sqrt{25}}{2 \cdot 1}$

Rewrite $25$ as $5^{2}$ .

$y = \frac{1 \pm \sqrt{5^{2}}}{2 \cdot 1}$

Pull terms out from under the radical, assuming positive real numbers.

$y = \frac{1 \pm 5}{2 \cdot 1}$

Multiply $2$ by $1$ .

$y = \frac{1 \pm 5}{2}$

Step 5

The final answer is the combination of both solutions.

$y = 3, - 2$

Solve Using the Quadratic Formula (y-3)(y+2)=0

Related Questions

Support LCMGCF.com by disabling your adblocker.