Solve for m 19m^2+5m-12=-6m^2

$19 m^{2} + 5 m - 12 = - 6 m^{2}$

Step 1

Move all terms containing $m$ to the left side of the equation.

Add $6 m^{2}$ to both sides of the equation.

$19 m^{2} + 5 m - 12 + 6 m^{2} = 0$

Add $19 m^{2}$ and $6 m^{2}$ .

$25 m^{2} + 5 m - 12 = 0$

Step 2

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 $a \cdot c = 25 \cdot - 12 = - 300$ and whose sum is $b = 5$ .

Factor $5$ out of $5 m$ .

$25 m^{2} + 5 (m) - 12 = 0$

Rewrite $5$ as $- 15$ plus $20$

$25 m^{2} + (- 15 + 20) m - 12 = 0$

Apply the distributive property.

$25 m^{2} - 15 m + 20 m - 12 = 0$

Factor out the greatest common factor from each group.

Group the first two terms and the last two terms.

$(25 m^{2} - 15 m) + 20 m - 12 = 0$

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

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

Factor the polynomial by factoring out the greatest common factor, $5 m - 3$ .

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

Step 3

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

$5 m - 3 = 0$

$5 m + 4 = 0$

Step 4

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

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

$5 m - 3 = 0$

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

Add $3$ to both sides of the equation.

$5 m = 3$

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

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

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Step 5

Set $5 m + 4$ equal to $0$ and solve for $m$ .

Set $5 m + 4$ equal to $0$ .

$5 m + 4 = 0$

Solve $5 m + 4 = 0$ for $m$ .

Subtract $4$ from both sides of the equation.

$5 m = - 4$

Divide each term in $5 m = - 4$ by $5$ and simplify.

Divide each term in $5 m = - 4$ by $5$ .

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

Simplify the left side.

Cancel the common factor of $5$ .

Cancel the common factor.

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

Divide $m$ by $1$ .

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

Simplify the right side.

Move the negative in front of the fraction.

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

Step 6

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

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

Step 7

The result can be shown in multiple forms.

Exact Form:

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

Decimal Form:

$m = 0.6, - 0.8$

Solve for m 19m^2+5m-12=-6m^2

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