Solve Using the Quadratic Formula (m+5)(3m+4)=3(m+2)-2

$(m + 5) (3 m + 4) = 3 (m + 2) - 2$

Step 1

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

Simplify the left side.

Simplify $(m + 5) (3 m + 4)$ .

Expand $(m + 5) (3 m + 4)$ using the FOIL Method.

Apply the distributive property.

$m (3 m + 4) + 5 (3 m + 4) = 3 (m + 2) - 2$

Apply the distributive property.

$m (3 m) + m \cdot 4 + 5 (3 m + 4) = 3 (m + 2) - 2$

Apply the distributive property.

$m (3 m) + m \cdot 4 + 5 (3 m) + 5 \cdot 4 = 3 (m + 2) - 2$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$3 m \cdot m + m \cdot 4 + 5 (3 m) + 5 \cdot 4 = 3 (m + 2) - 2$

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

Move $m$ .

$3 (m \cdot m) + m \cdot 4 + 5 (3 m) + 5 \cdot 4 = 3 (m + 2) - 2$

Multiply $m$ by $m$ .

$3 m^{2} + m \cdot 4 + 5 (3 m) + 5 \cdot 4 = 3 (m + 2) - 2$

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

$3 m^{2} + 4 \cdot m + 5 (3 m) + 5 \cdot 4 = 3 (m + 2) - 2$

Multiply $3$ by $5$ .

$3 m^{2} + 4 m + 15 m + 5 \cdot 4 = 3 (m + 2) - 2$

Multiply $5$ by $4$ .

$3 m^{2} + 4 m + 15 m + 20 = 3 (m + 2) - 2$

Add $4 m$ and $15 m$ .

$3 m^{2} + 19 m + 20 = 3 (m + 2) - 2$

Simplify the right side.

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

Simplify each term.

Apply the distributive property.

$3 m^{2} + 19 m + 20 = 3 m + 3 \cdot 2 - 2$

Multiply $3$ by $2$ .

$3 m^{2} + 19 m + 20 = 3 m + 6 - 2$

Subtract $2$ from $6$ .

$3 m^{2} + 19 m + 20 = 3 m + 4$

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

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

$3 m^{2} + 19 m + 20 - 3 m = 4$

Subtract $4$ from both sides of the equation.

$3 m^{2} + 19 m + 20 - 3 m - 4 = 0$

Simplify $3 m^{2} + 19 m + 20 - 3 m - 4$ .

Subtract $3 m$ from $19 m$ .

$3 m^{2} + 16 m + 20 - 4 = 0$

Subtract $4$ from $20$ .

$3 m^{2} + 16 m + 16 = 0$

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 $a = 3$ , $b = 16$ , and $c = 16$ into the quadratic formula and solve for $m$ .

$\frac{- 16 \pm \sqrt{16^{2} - 4 \cdot (3 \cdot 16)}}{2 \cdot 3}$

Step 4

Simplify.

Simplify the numerator.

Raise $16$ to the power of $2$ .

$m = \frac{- 16 \pm \sqrt{256 - 4 \cdot 3 \cdot 16}}{2 \cdot 3}$

Multiply $- 4 \cdot 3 \cdot 16$ .

Multiply $- 4$ by $3$ .

$m = \frac{- 16 \pm \sqrt{256 - 12 \cdot 16}}{2 \cdot 3}$

Multiply $- 12$ by $16$ .

$m = \frac{- 16 \pm \sqrt{256 - 192}}{2 \cdot 3}$

Subtract $192$ from $256$ .

$m = \frac{- 16 \pm \sqrt{64}}{2 \cdot 3}$

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

$m = \frac{- 16 \pm \sqrt{8^{2}}}{2 \cdot 3}$

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

$m = \frac{- 16 \pm 8}{2 \cdot 3}$

Multiply $2$ by $3$ .

$m = \frac{- 16 \pm 8}{6}$

Simplify $\frac{- 16 \pm 8}{6}$ .

$m = \frac{- 8 \pm 4}{3}$

Step 5

The final answer is the combination of both solutions.

$m = - \frac{4}{3}, - 4$

Solve Using the Quadratic Formula (m+5)(3m+4)=3(m+2)-2

Related Questions

Support LCMGCF.com by disabling your adblocker.