Precalculus Examples

$(y - 3) (y + 4) = 30$

Step 1

Move all terms to the left side of the equation and simplify.

Tap for more steps...

Step 1.1

Simplify the left side.

Tap for more steps...

Step 1.1.1

Simplify $(y - 3) (y + 4)$ .

Tap for more steps...

Step 1.1.1.1

Expand $(y - 3) (y + 4)$ using the FOIL Method.

Tap for more steps...

Step 1.1.1.1.1

Apply the distributive property.

$y (y + 4) - 3 (y + 4) = 30$

Step 1.1.1.1.2

Apply the distributive property.

$y \cdot y + y \cdot 4 - 3 (y + 4) = 30$

Step 1.1.1.1.3

Apply the distributive property.

$y \cdot y + y \cdot 4 - 3 y - 3 \cdot 4 = 30$

Step 1.1.1.2

Simplify and combine like terms.

Tap for more steps...

Step 1.1.1.2.1

Simplify each term.

Tap for more steps...

Step 1.1.1.2.1.1

Multiply $y$ by $y$ .

$y^{2} + y \cdot 4 - 3 y - 3 \cdot 4 = 30$

Step 1.1.1.2.1.2

Move $4$ to the left of $y$ .

$y^{2} + 4 \cdot y - 3 y - 3 \cdot 4 = 30$

Step 1.1.1.2.1.3

Multiply $- 3$ by $4$ .

$y^{2} + 4 y - 3 y - 12 = 30$

Step 1.1.1.2.2

Subtract $3 y$ from $4 y$ .

$y^{2} + y - 12 = 30$

Step 1.2

Subtract $30$ from both sides of the equation.

$y^{2} + y - 12 - 30 = 0$

Step 1.3

Subtract $30$ from $- 12$ .

$y^{2} + y - 42 = 0$

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 $c = - 42$ into the quadratic formula and solve for $y$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (1 \cdot - 42)}}{2 \cdot 1}$

Step 4

Simplify.

Tap for more steps...

Step 4.1

Simplify the numerator.

Tap for more steps...

Step 4.1.1

One to any power is one.

$y = \frac{- 1 \pm \sqrt{1 - 4 \cdot 1 \cdot - 42}}{2 \cdot 1}$

Step 4.1.2

Multiply $- 4 \cdot 1 \cdot - 42$ .

Tap for more steps...

Step 4.1.2.1

Multiply $- 4$ by $1$ .

$y = \frac{- 1 \pm \sqrt{1 - 4 \cdot - 42}}{2 \cdot 1}$

Step 4.1.2.2

Multiply $- 4$ by $- 42$ .

$y = \frac{- 1 \pm \sqrt{1 + 168}}{2 \cdot 1}$

Step 4.1.3

Add $1$ and $168$ .

$y = \frac{- 1 \pm \sqrt{169}}{2 \cdot 1}$

Step 4.1.4

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

$y = \frac{- 1 \pm \sqrt{13^{2}}}{2 \cdot 1}$

Step 4.1.5

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

$y = \frac{- 1 \pm 13}{2 \cdot 1}$

Step 4.2

Multiply $2$ by $1$ .

$y = \frac{- 1 \pm 13}{2}$

Step 5

The final answer is the combination of both solutions.

$y = 6, - 7$