Solve Using the Quadratic Formula (x+3)(2x-5)=0

$(x + 3) (2 x - 5) = 0$

Step 1

Simplify the left side.

Simplify $(x + 3) (2 x - 5)$ .

Expand $(x + 3) (2 x - 5)$ using the FOIL Method.

Apply the distributive property.

$x (2 x - 5) + 3 (2 x - 5) = 0$

Apply the distributive property.

$x (2 x) + x \cdot - 5 + 3 (2 x - 5) = 0$

Apply the distributive property.

$x (2 x) + x \cdot - 5 + 3 (2 x) + 3 \cdot - 5 = 0$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$2 x \cdot x + x \cdot - 5 + 3 (2 x) + 3 \cdot - 5 = 0$

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

Move $x$ .

$2 (x \cdot x) + x \cdot - 5 + 3 (2 x) + 3 \cdot - 5 = 0$

Multiply $x$ by $x$ .

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

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

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

Multiply $2$ by $3$ .

$2 x^{2} - 5 x + 6 x + 3 \cdot - 5 = 0$

Multiply $3$ by $- 5$ .

$2 x^{2} - 5 x + 6 x - 15 = 0$

Add $- 5 x$ and $6 x$ .

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

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 $a = 2$ , $b = 1$ , and $c = - 15$ into the quadratic formula and solve for $x$ .

$\frac{- 1 \pm \sqrt{1^{2} - 4 \cdot (2 \cdot - 15)}}{2 \cdot 2}$

Step 4

Simplify.

Simplify the numerator.

One to any power is one.

$x = \frac{- 1 \pm \sqrt{1 - 4 \cdot 2 \cdot - 15}}{2 \cdot 2}$

Multiply $- 4 \cdot 2 \cdot - 15$ .

Multiply $- 4$ by $2$ .

$x = \frac{- 1 \pm \sqrt{1 - 8 \cdot - 15}}{2 \cdot 2}$

Multiply $- 8$ by $- 15$ .

$x = \frac{- 1 \pm \sqrt{1 + 120}}{2 \cdot 2}$

Add $1$ and $120$ .

$x = \frac{- 1 \pm \sqrt{121}}{2 \cdot 2}$

Rewrite $121$ as $11^{2}$ .

$x = \frac{- 1 \pm \sqrt{11^{2}}}{2 \cdot 2}$

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

$x = \frac{- 1 \pm 11}{2 \cdot 2}$

Multiply $2$ by $2$ .

$x = \frac{- 1 \pm 11}{4}$

Step 5

The final answer is the combination of both solutions.

$x = \frac{5}{2}, - 3$

Solve Using the Quadratic Formula (x+3)(2x-5)=0

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