m^2=-10-7m

Solution for m^2=-10-7m equation:

Simplifying
m2 = -10 + -7m

Solving
m2 = -10 + -7m

Solving for variable 'm'.

Reorder the terms:
10 + 7m + m2 = -10 + -7m + 10 + 7m

Reorder the terms:
10 + 7m + m2 = -10 + 10 + -7m + 7m

Combine like terms: -10 + 10 = 0
10 + 7m + m2 = 0 + -7m + 7m
10 + 7m + m2 = -7m + 7m

Combine like terms: -7m + 7m = 0
10 + 7m + m2 = 0

Factor a trinomial.
(5 + m)(2 + m) = 0

Subproblem 1
Set the factor '(5 + m)' equal to zero and attempt to solve:

Simplifying
5 + m = 0

Solving
5 + m = 0

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

Add '-5' to each side of the equation.
5 + -5 + m = 0 + -5

Combine like terms: 5 + -5 = 0
0 + m = 0 + -5
m = 0 + -5

Combine like terms: 0 + -5 = -5
m = -5

Simplifying
m = -5
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 = {-5, -2}