m(m+12)-10(m+12)=0

Solution for m(m+12)-10(m+12)=0 equation:

Simplifying
m(m + 12) + -10(m + 12) = 0

Reorder the terms:
m(12 + m) + -10(m + 12) = 0
(12 * m + m * m) + -10(m + 12) = 0
(12m + m2) + -10(m + 12) = 0

Reorder the terms:
12m + m2 + -10(12 + m) = 0
12m + m2 + (12 * -10 + m * -10) = 0
12m + m2 + (-120 + -10m) = 0

Reorder the terms:
-120 + 12m + -10m + m2 = 0

Combine like terms: 12m + -10m = 2m
-120 + 2m + m2 = 0

Solving
-120 + 2m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-12 + -1m)(10 + -1m) = 0

Subproblem 1
Set the factor '(-12 + -1m)' equal to zero and attempt to solve:

Simplifying
-12 + -1m = 0

Solving
-12 + -1m = 0

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

Add '12' to each side of the equation.
-12 + 12 + -1m = 0 + 12

Combine like terms: -12 + 12 = 0
0 + -1m = 0 + 12
-1m = 0 + 12

Combine like terms: 0 + 12 = 12
-1m = 12

Divide each side by '-1'.
m = -12

Simplifying
m = -12
Subproblem 2
Set the factor '(10 + -1m)' equal to zero and attempt to solve:

Simplifying
10 + -1m = 0

Solving
10 + -1m = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1m = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1m = 0 + -10
-1m = 0 + -10

Combine like terms: 0 + -10 = -10
-1m = -10

Divide each side by '-1'.
m = 10

Simplifying
m = 10
Solution
m = {-12, 10}