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

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

Step 1

Simplify the left side.

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

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

Apply the distributive property.

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

Apply the distributive property.

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

Apply the distributive property.

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

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

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

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

Move $x$ .

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

Multiply $x$ by $x$ .

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

Move $5$ to the left of $x$ .

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

Multiply $3$ by $- 1$ .

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

Multiply $- 1$ by $5$ .

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

Subtract $3 x$ from $5 x$ .

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

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 $a = 3$ , $b = 2$ , and $c = - 5$ into the quadratic formula and solve for $x$ .

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

Step 4

Simplify.

Simplify the numerator.

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

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

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

Multiply $- 4$ by $3$ .

$x = \frac{- 2 \pm \sqrt{4 - 12 \cdot - 5}}{2 \cdot 3}$

Multiply $- 12$ by $- 5$ .

$x = \frac{- 2 \pm \sqrt{4 + 60}}{2 \cdot 3}$

Add $4$ and $60$ .

$x = \frac{- 2 \pm \sqrt{64}}{2 \cdot 3}$

Rewrite $64$ as $8^{2}$ .

$x = \frac{- 2 \pm \sqrt{8^{2}}}{2 \cdot 3}$

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

$x = \frac{- 2 \pm 8}{2 \cdot 3}$

Multiply $2$ by $3$ .

$x = \frac{- 2 \pm 8}{6}$

Simplify $\frac{- 2 \pm 8}{6}$ .

$x = \frac{- 1 \pm 4}{3}$

Step 5

The final answer is the combination of both solutions.

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

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

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