Solve for m (m+3)(m-4)=-6

$(m + 3) (m - 4) = - 6$

Step 1

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

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

Apply the distributive property.

$m (m - 4) + 3 (m - 4) = - 6$

Apply the distributive property.

$m \cdot m + m \cdot - 4 + 3 (m - 4) = - 6$

Apply the distributive property.

$m \cdot m + m \cdot - 4 + 3 m + 3 \cdot - 4 = - 6$

Simplify and combine like terms.

Simplify each term.

Multiply $m$ by $m$ .

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

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

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

Multiply $3$ by $- 4$ .

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

Add $- 4 m$ and $3 m$ .

$m^{2} - m - 12 = - 6$

Step 2

Add $6$ to both sides of the equation.

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

Step 3

Add $- 12$ and $6$ .

$m^{2} - m - 6 = 0$

Step 4

Factor $m^{2} - m - 6$ using the AC method.

Consider the form $x^{2} + b x + c$ . Find a pair of integers whose product is $c$ and whose sum is $b$ . In this case, whose product is $- 6$ and whose sum is $- 1$ .

$- 3, 2$

Write the factored form using these integers.

$(m - 3) (m + 2) = 0$

Step 5

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

$m - 3 = 0$

$m + 2 = 0$

Step 6

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

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

$m - 3 = 0$

Add $3$ to both sides of the equation.

$m = 3$

Step 7

Set $m + 2$ equal to $0$ and solve for $m$ .

Set $m + 2$ equal to $0$ .

$m + 2 = 0$

Subtract $2$ from both sides of the equation.

$m = - 2$

Step 8

The final solution is all the values that make $(m - 3) (m + 2) = 0$ true.

$m = 3, - 2$

Solve for m (m+3)(m-4)=-6

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