3(4m^2+2)+27m=10m

Solution for 3(4m^2+2)+27m=10m equation:

Simplifying
3(4m2 + 2) + 27m = 10m

Reorder the terms:
3(2 + 4m2) + 27m = 10m
(2 * 3 + 4m2 * 3) + 27m = 10m
(6 + 12m2) + 27m = 10m

Reorder the terms:
6 + 27m + 12m2 = 10m

Solving
6 + 27m + 12m2 = 10m

Solving for variable 'm'.

Reorder the terms:
6 + 27m + -10m + 12m2 = 10m + -10m

Combine like terms: 27m + -10m = 17m
6 + 17m + 12m2 = 10m + -10m

Combine like terms: 10m + -10m = 0
6 + 17m + 12m2 = 0

Factor a trinomial.
(3 + 4m)(2 + 3m) = 0

Subproblem 1
Set the factor '(3 + 4m)' equal to zero and attempt to solve:

Simplifying
3 + 4m = 0

Solving
3 + 4m = 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 + 4m = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4m = 0 + -3
4m = 0 + -3

Combine like terms: 0 + -3 = -3
4m = -3

Divide each side by '4'.
m = -0.75

Simplifying
m = -0.75
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 = {-0.75, -0.6666666667}