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

Solution for (m+3)(m-4)=-6 equation:

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

Reorder the terms:
(3 + m)(m + -4) = -6

Reorder the terms:
(3 + m)(-4 + m) = -6

Multiply (3 + m) * (-4 + m)
(3(-4 + m) + m(-4 + m)) = -6
((-4 * 3 + m * 3) + m(-4 + m)) = -6
((-12 + 3m) + m(-4 + m)) = -6
(-12 + 3m + (-4 * m + m * m)) = -6
(-12 + 3m + (-4m + m2)) = -6

Combine like terms: 3m + -4m = -1m
(-12 + -1m + m2) = -6

Solving
-12 + -1m + m2 = -6

Solving for variable 'm'.

Reorder the terms:
-12 + 6 + -1m + m2 = -6 + 6

Combine like terms: -12 + 6 = -6
-6 + -1m + m2 = -6 + 6

Combine like terms: -6 + 6 = 0
-6 + -1m + m2 = 0

Factor a trinomial.
(-2 + -1m)(3 + -1m) = 0

Subproblem 1
Set the factor '(-2 + -1m)' equal to zero and attempt to solve:

Simplifying
-2 + -1m = 0

Solving
-2 + -1m = 0

Move all terms containing m to the left, all other terms to the right.

Add '2' to each side of the equation.
-2 + 2 + -1m = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1m = 0 + 2
-1m = 0 + 2

Combine like terms: 0 + 2 = 2
-1m = 2

Divide each side by '-1'.
m = -2

Simplifying
m = -2
Subproblem 2
Set the factor '(3 + -1m)' equal to zero and attempt to solve:

Simplifying
3 + -1m = 0

Solving
3 + -1m = 0

Move all terms containing m to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + -1m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1m = 0 + -3
-1m = 0 + -3

Combine like terms: 0 + -3 = -3
-1m = -3

Divide each side by '-1'.
m = 3

Simplifying
m = 3
Solution
m = {-2, 3}