Solve Using the Quadratic Formula (3x-1)(x+5)=0

$(3 x - 1) (x + 5) = 0$

Step 1

Simplify the left side.

Simplify $(3 x - 1) (x + 5)$ .

Expand $(3 x - 1) (x + 5)$ using the FOIL Method.

Apply the distributive property.

$3 x (x + 5) - 1 (x + 5) = 0$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 5 - 1 (x + 5) = 0$

Apply the distributive property.

$3 x \cdot x + 3 x \cdot 5 - 1 x - 1 \cdot 5 = 0$

Simplify and combine like terms.

Simplify each term.

Multiply $x$ by $x$ by adding the exponents.

Move $x$ .

$3 (x \cdot x) + 3 x \cdot 5 - 1 x - 1 \cdot 5 = 0$

Multiply $x$ by $x$ .

$3 x^{2} + 3 x \cdot 5 - 1 x - 1 \cdot 5 = 0$

Multiply $5$ by $3$ .

$3 x^{2} + 15 x - 1 x - 1 \cdot 5 = 0$

Rewrite $- 1 x$ as $- x$ .

$3 x^{2} + 15 x - x - 1 \cdot 5 = 0$

Multiply $- 1$ by $5$ .

$3 x^{2} + 15 x - x - 5 = 0$

Subtract $x$ from $15 x$ .

$3 x^{2} + 14 x - 5 = 0$

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 $a = 3$ , $b = 14$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

$\frac{- 14 \pm \sqrt{14^{2} - 4 \cdot (3 \cdot - 5)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $14$ to the power of $2$ .

$x = \frac{- 14 \pm \sqrt{196 - 4 \cdot 3 \cdot - 5}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 5$ .

Multiply $- 4$ by $3$ .

$x = \frac{- 14 \pm \sqrt{196 - 12 \cdot - 5}}{2 \cdot 3}$

Multiply $- 12$ by $- 5$ .

$x = \frac{- 14 \pm \sqrt{196 + 60}}{2 \cdot 3}$

Add $196$ and $60$ .

$x = \frac{- 14 \pm \sqrt{256}}{2 \cdot 3}$

Rewrite $256$ as $16^{2}$ .

$x = \frac{- 14 \pm \sqrt{16^{2}}}{2 \cdot 3}$

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

$x = \frac{- 14 \pm 16}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 14 \pm 16}{6}$

Simplify $\frac{- 14 \pm 16}{6}$ .

$x = \frac{- 7 \pm 8}{3}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{1}{3}, - 5$

Solve Using the Quadratic Formula (3x-1)(x+5)=0

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