12m^2=5m+2

Solution for 12m^2=5m+2 equation:

Simplifying
12m2 = 5m + 2

Reorder the terms:
12m2 = 2 + 5m

Solving
12m2 = 2 + 5m

Solving for variable 'm'.

Reorder the terms:
-2 + -5m + 12m2 = 2 + 5m + -2 + -5m

Reorder the terms:
-2 + -5m + 12m2 = 2 + -2 + 5m + -5m

Combine like terms: 2 + -2 = 0
-2 + -5m + 12m2 = 0 + 5m + -5m
-2 + -5m + 12m2 = 5m + -5m

Combine like terms: 5m + -5m = 0
-2 + -5m + 12m2 = 0

Factor a trinomial.
(-1 + -4m)(2 + -3m) = 0

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

Simplifying
-1 + -4m = 0

Solving
-1 + -4m = 0

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

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

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

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

Divide each side by '-4'.
m = -0.25

Simplifying
m = -0.25
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 = {-0.25, 0.6666666667}