Solve Using the Quadratic Formula (2y+5)(y-4)=0

$(2 y + 5) (y - 4) = 0$

Step 1

Simplify the left side.

Simplify $(2 y + 5) (y - 4)$ .

Expand $(2 y + 5) (y - 4)$ using the FOIL Method.

Apply the distributive property.

$2 y (y - 4) + 5 (y - 4) = 0$

Apply the distributive property.

$2 y \cdot y + 2 y \cdot - 4 + 5 (y - 4) = 0$

Apply the distributive property.

$2 y \cdot y + 2 y \cdot - 4 + 5 y + 5 \cdot - 4 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $y$ by $y$ by adding the exponents.

Move $y$ .

$2 (y \cdot y) + 2 y \cdot - 4 + 5 y + 5 \cdot - 4 = 0$

Multiply $y$ by $y$ .

$2 y^{2} + 2 y \cdot - 4 + 5 y + 5 \cdot - 4 = 0$

Multiply $- 4$ by $2$ .

$2 y^{2} - 8 y + 5 y + 5 \cdot - 4 = 0$

Multiply $5$ by $- 4$ .

$2 y^{2} - 8 y + 5 y - 20 = 0$

Add $- 8 y$ and $5 y$ .

$2 y^{2} - 3 y - 20 = 0$

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 $a = 2$ , $b = - 3$ , and $c = - 20$ into the quadratic formula and solve for $y$ .

$\frac{3 \pm \sqrt{{(- 3)}^{2} - 4 \cdot (2 \cdot - 20)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 3$ to the power of $2$ .

$y = \frac{3 \pm \sqrt{9 - 4 \cdot 2 \cdot - 20}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 20$ .

Multiply $- 4$ by $2$ .

$y = \frac{3 \pm \sqrt{9 - 8 \cdot - 20}}{2 \cdot 2}$

Multiply $- 8$ by $- 20$ .

$y = \frac{3 \pm \sqrt{9 + 160}}{2 \cdot 2}$

Add $9$ and $160$ .

$y = \frac{3 \pm \sqrt{169}}{2 \cdot 2}$

Rewrite $169$ as $13^{2}$ .

$y = \frac{3 \pm \sqrt{13^{2}}}{2 \cdot 2}$

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

$y = \frac{3 \pm 13}{2 \cdot 2}$

Multiply $2$ by $2$ .

$y = \frac{3 \pm 13}{4}$

Step 5

The final answer is the combination of both solutions.

$y = 4, - \frac{5}{2}$

Solve Using the Quadratic Formula (2y+5)(y-4)=0

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