m^2+20m+84=0

Solution for m^2+20m+84=0 equation:

Simplifying
m2 + 20m + 84 = 0

Reorder the terms:
84 + 20m + m2 = 0

Solving
84 + 20m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(14 + m)(6 + m) = 0

Subproblem 1
Set the factor '(14 + m)' equal to zero and attempt to solve:

Simplifying
14 + m = 0

Solving
14 + m = 0

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

Add '-14' to each side of the equation.
14 + -14 + m = 0 + -14

Combine like terms: 14 + -14 = 0
0 + m = 0 + -14
m = 0 + -14

Combine like terms: 0 + -14 = -14
m = -14

Simplifying
m = -14
Subproblem 2
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
Solution
m = {-14, -6}