Solve Using the Quadratic Formula (m+1)(4m-10)=3(m+4)-9

$(m + 1) (4 m - 10) = 3 (m + 4) - 9$

Step 1

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

Simplify the left side.

Simplify $(m + 1) (4 m - 10)$ .

Expand $(m + 1) (4 m - 10)$ using the FOIL Method.

Apply the distributive property.

$m (4 m - 10) + 1 (4 m - 10) = 3 (m + 4) - 9$

Apply the distributive property.

$m (4 m) + m \cdot - 10 + 1 (4 m - 10) = 3 (m + 4) - 9$

Apply the distributive property.

$m (4 m) + m \cdot - 10 + 1 (4 m) + 1 \cdot - 10 = 3 (m + 4) - 9$

Simplify and combine like terms.

Simplify each term.

Rewrite using the commutative property of multiplication.

$4 m \cdot m + m \cdot - 10 + 1 (4 m) + 1 \cdot - 10 = 3 (m + 4) - 9$

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

Move $m$ .

$4 (m \cdot m) + m \cdot - 10 + 1 (4 m) + 1 \cdot - 10 = 3 (m + 4) - 9$

Multiply $m$ by $m$ .

$4 m^{2} + m \cdot - 10 + 1 (4 m) + 1 \cdot - 10 = 3 (m + 4) - 9$

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

$4 m^{2} - 10 \cdot m + 1 (4 m) + 1 \cdot - 10 = 3 (m + 4) - 9$

Multiply $4 m$ by $1$ .

$4 m^{2} - 10 m + 4 m + 1 \cdot - 10 = 3 (m + 4) - 9$

Multiply $- 10$ by $1$ .

$4 m^{2} - 10 m + 4 m - 10 = 3 (m + 4) - 9$

Add $- 10 m$ and $4 m$ .

$4 m^{2} - 6 m - 10 = 3 (m + 4) - 9$

Simplify the right side.

Simplify $3 (m + 4) - 9$ .

Simplify each term.

Apply the distributive property.

$4 m^{2} - 6 m - 10 = 3 m + 3 \cdot 4 - 9$

Multiply $3$ by $4$ .

$4 m^{2} - 6 m - 10 = 3 m + 12 - 9$

Subtract $9$ from $12$ .

$4 m^{2} - 6 m - 10 = 3 m + 3$

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

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

$4 m^{2} - 6 m - 10 - 3 m = 3$

Subtract $3$ from both sides of the equation.

$4 m^{2} - 6 m - 10 - 3 m - 3 = 0$

Simplify $4 m^{2} - 6 m - 10 - 3 m - 3$ .

Subtract $3 m$ from $- 6 m$ .

$4 m^{2} - 9 m - 10 - 3 = 0$

Subtract $3$ from $- 10$ .

$4 m^{2} - 9 m - 13 = 0$

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 $a = 4$ , $b = - 9$ , and $c = - 13$ into the quadratic formula and solve for $m$ .

$\frac{9 \pm \sqrt{{(- 9)}^{2} - 4 \cdot (4 \cdot - 13)}}{2 \cdot 4}$

Step 4

Simplify.

Simplify the numerator.

Raise $- 9$ to the power of $2$ .

$m = \frac{9 \pm \sqrt{81 - 4 \cdot 4 \cdot - 13}}{2 \cdot 4}$

Multiply $- 4 \cdot 4 \cdot - 13$ .

Multiply $- 4$ by $4$ .

$m = \frac{9 \pm \sqrt{81 - 16 \cdot - 13}}{2 \cdot 4}$

Multiply $- 16$ by $- 13$ .

$m = \frac{9 \pm \sqrt{81 + 208}}{2 \cdot 4}$

Add $81$ and $208$ .

$m = \frac{9 \pm \sqrt{289}}{2 \cdot 4}$

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

$m = \frac{9 \pm \sqrt{17^{2}}}{2 \cdot 4}$

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

$m = \frac{9 \pm 17}{2 \cdot 4}$

Multiply $2$ by $4$ .

$m = \frac{9 \pm 17}{8}$

Step 5

The final answer is the combination of both solutions.

$m = \frac{13}{4}, - 1$

Solve Using the Quadratic Formula (m+1)(4m-10)=3(m+4)-9

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