m(m+6)-4(m+6)=0

Solution for m(m+6)-4(m+6)=0 equation:

Simplifying
m(m + 6) + -4(m + 6) = 0

Reorder the terms:
m(6 + m) + -4(m + 6) = 0
(6 * m + m * m) + -4(m + 6) = 0
(6m + m2) + -4(m + 6) = 0

Reorder the terms:
6m + m2 + -4(6 + m) = 0
6m + m2 + (6 * -4 + m * -4) = 0
6m + m2 + (-24 + -4m) = 0

Reorder the terms:
-24 + 6m + -4m + m2 = 0

Combine like terms: 6m + -4m = 2m
-24 + 2m + m2 = 0

Solving
-24 + 2m + m2 = 0

Solving for variable 'm'.

Factor a trinomial.
(-6 + -1m)(4 + -1m) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(4 + -1m)' equal to zero and attempt to solve:

Simplifying
4 + -1m = 0

Solving
4 + -1m = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1m = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1m = 0 + -4
-1m = 0 + -4

Combine like terms: 0 + -4 = -4
-1m = -4

Divide each side by '-1'.
m = 4

Simplifying
m = 4
Solution
m = {-6, 4}