7m^2+7m=42

Solution for 7m^2+7m=42 equation:

Simplifying
7m2 + 7m = 42

Reorder the terms:
7m + 7m2 = 42

Solving
7m + 7m2 = 42

Solving for variable 'm'.

Reorder the terms:
-42 + 7m + 7m2 = 42 + -42

Combine like terms: 42 + -42 = 0
-42 + 7m + 7m2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-6 + m + m2) = 0

Factor a trinomial.
7((-3 + -1m)(2 + -1m)) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-3 + -1m)' equal to zero and attempt to solve:

Simplifying
-3 + -1m = 0

Solving
-3 + -1m = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1m = 0 + 3
-1m = 0 + 3

Combine like terms: 0 + 3 = 3
-1m = 3

Divide each side by '-1'.
m = -3

Simplifying
m = -3
Subproblem 2
Set the factor '(2 + -1m)' equal to zero and attempt to solve:

Simplifying
2 + -1m = 0

Solving
2 + -1m = 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 + -1m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1m = 0 + -2
-1m = 0 + -2

Combine like terms: 0 + -2 = -2
-1m = -2

Divide each side by '-1'.
m = 2

Simplifying
m = 2
Solution
m = {-3, 2}