7m^2+56m=-84

Solution for 7m^2+56m=-84 equation:

Simplifying
7m2 + 56m = -84

Reorder the terms:
56m + 7m2 = -84

Solving
56m + 7m2 = -84

Solving for variable 'm'.

Reorder the terms:
84 + 56m + 7m2 = -84 + 84

Combine like terms: -84 + 84 = 0
84 + 56m + 7m2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(12 + 8m + m2) = 0

Factor a trinomial.
7((6 + m)(2 + m)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(6 + m)' equal to zero and attempt to solve:

Simplifying
6 + m = 0

Solving
6 + m = 0

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

Add '-6' to each side of the equation.
6 + -6 + m = 0 + -6

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

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

Simplifying
m = -6
Subproblem 2
Set the factor '(2 + m)' equal to zero and attempt to solve:

Simplifying
2 + m = 0

Solving
2 + m = 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 + m = 0 + -2

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

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

Simplifying
m = -2
Solution
m = {-6, -2}