Solve for m 12m^2+11m=15

$12 m^{2} + 11 m = 15$

Subtract $15$ from both sides of the equation.

$12 m^{2} + 11 m - 15 = 0$

Factor by grouping.

For a polynomial of the form $a x^{2} + b x + c$ , rewrite the middle term as a sum of two terms whose product is $a \cdot c = 12 \cdot - 15 = - 180$ and whose sum is $b = 11$ .

Factor $11$ out of $11 m$ .

$12 m^{2} + 11 (m) - 15 = 0$

Rewrite $11$ as $- 9$ plus $20$

$12 m^{2} + (- 9 + 20) m - 15 = 0$

Apply the distributive property.

$12 m^{2} - 9 m + 20 m - 15 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(12 m^{2} - 9 m) + 20 m - 15 = 0$

Factor out the greatest common factor (GCF) from each group.

$3 m (4 m - 3) + 5 (4 m - 3) = 0$

Factor the polynomial by factoring out the greatest common factor, $4 m - 3$ .

$(4 m - 3) (3 m + 5) = 0$

If any individual factor on the left side of the equation is equal to $0$ , the entire expression will be equal to $0$ .

$4 m - 3 = 0$

$3 m + 5 = 0$

Set $4 m - 3$ equal to $0$ and solve for $m$ .

Set $4 m - 3$ equal to $0$ .

$4 m - 3 = 0$

Solve $4 m - 3 = 0$ for $m$ .

Add $3$ to both sides of the equation.

$4 m = 3$

Divide each term in $4 m = 3$ by $4$ and simplify.

Divide each term in $4 m = 3$ by $4$ .

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

Simplify the left side.

Cancel the common factor of $4$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Set $3 m + 5$ equal to $0$ and solve for $m$ .

Set $3 m + 5$ equal to $0$ .

$3 m + 5 = 0$

Solve $3 m + 5 = 0$ for $m$ .

Subtract $5$ from both sides of the equation.

$3 m = - 5$

Divide each term in $3 m = - 5$ by $3$ and simplify.

Divide each term in $3 m = - 5$ by $3$ .

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

Simplify the left side.

Cancel the common factor of $3$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

The final solution is all the values that make $(4 m - 3) (3 m + 5) = 0$ true.

$m = \frac{3}{4}, - \frac{5}{3}$

The result can be shown in multiple forms.

Exact Form:

$m = \frac{3}{4}, - \frac{5}{3}$

Decimal Form:

$m = 0.75, - 1.\overline{6}$

Mixed Number Form:

$m = \frac{3}{4}, - 1 \frac{2}{3}$

Solve for m 12m^2+11m=15

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