12+2m=7m(m+6)

Solution for 12+2m=7m(m+6) equation:

Simplifying
12 + 2m = 7m(m + 6)

Reorder the terms:
12 + 2m = 7m(6 + m)
12 + 2m = (6 * 7m + m * 7m)
12 + 2m = (42m + 7m2)

Solving
12 + 2m = 42m + 7m2

Solving for variable 'm'.

Combine like terms: 2m + -42m = -40m
12 + -40m + -7m2 = 42m + 7m2 + -42m + -7m2

Reorder the terms:
12 + -40m + -7m2 = 42m + -42m + 7m2 + -7m2

Combine like terms: 42m + -42m = 0
12 + -40m + -7m2 = 0 + 7m2 + -7m2
12 + -40m + -7m2 = 7m2 + -7m2

Combine like terms: 7m2 + -7m2 = 0
12 + -40m + -7m2 = 0

Factor a trinomial.
(2 + -7m)(6 + m) = 0

Subproblem 1
Set the factor '(2 + -7m)' equal to zero and attempt to solve:

Simplifying
2 + -7m = 0

Solving
2 + -7m = 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 + -7m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7m = 0 + -2
-7m = 0 + -2

Combine like terms: 0 + -2 = -2
-7m = -2

Divide each side by '-7'.
m = 0.2857142857

Simplifying
m = 0.2857142857
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 = {0.2857142857, -6}