6m(m+3)=5m-6

Solution for 6m(m+3)=5m-6 equation:

Simplifying
6m(m + 3) = 5m + -6

Reorder the terms:
6m(3 + m) = 5m + -6
(3 * 6m + m * 6m) = 5m + -6
(18m + 6m2) = 5m + -6

Reorder the terms:
18m + 6m2 = -6 + 5m

Solving
18m + 6m2 = -6 + 5m

Solving for variable 'm'.

Reorder the terms:
6 + 18m + -5m + 6m2 = -6 + 5m + 6 + -5m

Combine like terms: 18m + -5m = 13m
6 + 13m + 6m2 = -6 + 5m + 6 + -5m

Reorder the terms:
6 + 13m + 6m2 = -6 + 6 + 5m + -5m

Combine like terms: -6 + 6 = 0
6 + 13m + 6m2 = 0 + 5m + -5m
6 + 13m + 6m2 = 5m + -5m

Combine like terms: 5m + -5m = 0
6 + 13m + 6m2 = 0

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

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

Simplifying
3 + 2m = 0

Solving
3 + 2m = 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 + 2m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2m = 0 + -3
2m = 0 + -3

Combine like terms: 0 + -3 = -3
2m = -3

Divide each side by '2'.
m = -1.5

Simplifying
m = -1.5
Subproblem 2
Set the factor '(2 + 3m)' equal to zero and attempt to solve:

Simplifying
2 + 3m = 0

Solving
2 + 3m = 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 + 3m = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 3m = 0 + -2
3m = 0 + -2

Combine like terms: 0 + -2 = -2
3m = -2

Divide each side by '3'.
m = -0.6666666667

Simplifying
m = -0.6666666667
Solution
m = {-1.5, -0.6666666667}