m^2=m+30

Solution for m^2=m+30 equation:

Simplifying
m2 = m + 30

Reorder the terms:
m2 = 30 + m

Solving
m2 = 30 + m

Solving for variable 'm'.

Reorder the terms:
-30 + -1m + m2 = 30 + m + -30 + -1m

Reorder the terms:
-30 + -1m + m2 = 30 + -30 + m + -1m

Combine like terms: 30 + -30 = 0
-30 + -1m + m2 = 0 + m + -1m
-30 + -1m + m2 = m + -1m

Combine like terms: m + -1m = 0
-30 + -1m + m2 = 0

Factor a trinomial.
(-5 + -1m)(6 + -1m) = 0

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

Simplifying
-5 + -1m = 0

Solving
-5 + -1m = 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 + -1m = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1m = 0 + 5
-1m = 0 + 5

Combine like terms: 0 + 5 = 5
-1m = 5

Divide each side by '-1'.
m = -5

Simplifying
m = -5
Subproblem 2
Set the factor '(6 + -1m)' equal to zero and attempt to solve:

Simplifying
6 + -1m = 0

Solving
6 + -1m = 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 + -1m = 0 + -6

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

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

Divide each side by '-1'.
m = 6

Simplifying
m = 6
Solution
m = {-5, 6}