3m^2=6-7m

Solution for 3m^2=6-7m equation:

Simplifying
3m2 = 6 + -7m

Solving
3m2 = 6 + -7m

Solving for variable 'm'.

Reorder the terms:
-6 + 7m + 3m2 = 6 + -7m + -6 + 7m

Reorder the terms:
-6 + 7m + 3m2 = 6 + -6 + -7m + 7m

Combine like terms: 6 + -6 = 0
-6 + 7m + 3m2 = 0 + -7m + 7m
-6 + 7m + 3m2 = -7m + 7m

Combine like terms: -7m + 7m = 0
-6 + 7m + 3m2 = 0

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

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

Simplifying
-3 + -1m = 0

Solving
-3 + -1m = 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 + -1m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1m = 0 + 3
-1m = 0 + 3

Combine like terms: 0 + 3 = 3
-1m = 3

Divide each side by '-1'.
m = -3

Simplifying
m = -3
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 = {-3, 0.6666666667}