m^2=42-m

Solution for m^2=42-m equation:

Simplifying
m2 = 42 + -1m

Solving
m2 = 42 + -1m

Solving for variable 'm'.

Reorder the terms:
-42 + m + m2 = 42 + -1m + -42 + m

Reorder the terms:
-42 + m + m2 = 42 + -42 + -1m + m

Combine like terms: 42 + -42 = 0
-42 + m + m2 = 0 + -1m + m
-42 + m + m2 = -1m + m

Combine like terms: -1m + m = 0
-42 + m + m2 = 0

Factor a trinomial.
(-7 + -1m)(6 + -1m) = 0

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

Simplifying
-7 + -1m = 0

Solving
-7 + -1m = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1m = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1m = 0 + 7
-1m = 0 + 7

Combine like terms: 0 + 7 = 7
-1m = 7

Divide each side by '-1'.
m = -7

Simplifying
m = -7
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 = {-7, 6}