Solve Using the Quadratic Formula (m+2)(3m+10)=3(m+5)+15

$(m + 2) (3 m + 10) = 3 (m + 5) + 15$

Step 1

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

Simplify the left side.

Simplify $(m + 2) (3 m + 10)$ .

Expand $(m + 2) (3 m + 10)$ using the FOIL Method.

Apply the distributive property.

$m (3 m + 10) + 2 (3 m + 10) = 3 (m + 5) + 15$

Apply the distributive property.

$m (3 m) + m \cdot 10 + 2 (3 m + 10) = 3 (m + 5) + 15$

Apply the distributive property.

$m (3 m) + m \cdot 10 + 2 (3 m) + 2 \cdot 10 = 3 (m + 5) + 15$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 m \cdot m + m \cdot 10 + 2 (3 m) + 2 \cdot 10 = 3 (m + 5) + 15$

Multiply $m$ by $m$ by adding the exponents.

Move $m$ .

$3 (m \cdot m) + m \cdot 10 + 2 (3 m) + 2 \cdot 10 = 3 (m + 5) + 15$

Multiply $m$ by $m$ .

$3 m^{2} + m \cdot 10 + 2 (3 m) + 2 \cdot 10 = 3 (m + 5) + 15$

Move $10$ to the left of $m$ .

$3 m^{2} + 10 \cdot m + 2 (3 m) + 2 \cdot 10 = 3 (m + 5) + 15$

Multiply $3$ by $2$ .

$3 m^{2} + 10 m + 6 m + 2 \cdot 10 = 3 (m + 5) + 15$

Multiply $2$ by $10$ .

$3 m^{2} + 10 m + 6 m + 20 = 3 (m + 5) + 15$

Add $10 m$ and $6 m$ .

$3 m^{2} + 16 m + 20 = 3 (m + 5) + 15$

Simplify the right side.

Simplify $3 (m + 5) + 15$ .

Simplify each term.

Apply the distributive property.

$3 m^{2} + 16 m + 20 = 3 m + 3 \cdot 5 + 15$

Multiply $3$ by $5$ .

$3 m^{2} + 16 m + 20 = 3 m + 15 + 15$

Add $15$ and $15$ .

$3 m^{2} + 16 m + 20 = 3 m + 30$

Move all the expressions to the left side of the equation.

Subtract $3 m$ from both sides of the equation.

$3 m^{2} + 16 m + 20 - 3 m = 30$

Subtract $30$ from both sides of the equation.

$3 m^{2} + 16 m + 20 - 3 m - 30 = 0$

Simplify $3 m^{2} + 16 m + 20 - 3 m - 30$ .

Subtract $3 m$ from $16 m$ .

$3 m^{2} + 13 m + 20 - 30 = 0$

Subtract $30$ from $20$ .

$3 m^{2} + 13 m - 10 = 0$

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 $a = 3$ , $b = 13$ , and $c = - 10$ into the quadratic formula and solve for $m$ .

$\frac{- 13 \pm \sqrt{13^{2} - 4 \cdot (3 \cdot - 10)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $13$ to the power of $2$ .

$m = \frac{- 13 \pm \sqrt{169 - 4 \cdot 3 \cdot - 10}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot - 10$ .

Multiply $- 4$ by $3$ .

$m = \frac{- 13 \pm \sqrt{169 - 12 \cdot - 10}}{2 \cdot 3}$

Multiply $- 12$ by $- 10$ .

$m = \frac{- 13 \pm \sqrt{169 + 120}}{2 \cdot 3}$

Add $169$ and $120$ .

$m = \frac{- 13 \pm \sqrt{289}}{2 \cdot 3}$

Rewrite $289$ as $17^{2}$ .

$m = \frac{- 13 \pm \sqrt{17^{2}}}{2 \cdot 3}$

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

$m = \frac{- 13 \pm 17}{2 \cdot 3}$

Multiply $2$ by $3$ .

$m = \frac{- 13 \pm 17}{6}$

Step 5

The final answer is the combination of both solutions.

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

Solve Using the Quadratic Formula (m+2)(3m+10)=3(m+5)+15

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