2m^2+39m-2=40m-4m^2

Solution for 2m^2+39m-2=40m-4m^2 equation:

Simplifying
2m2 + 39m + -2 = 40m + -4m2

Reorder the terms:
-2 + 39m + 2m2 = 40m + -4m2

Solving
-2 + 39m + 2m2 = 40m + -4m2

Solving for variable 'm'.

Reorder the terms:
-2 + 39m + -40m + 2m2 + 4m2 = 40m + -4m2 + -40m + 4m2

Combine like terms: 39m + -40m = -1m
-2 + -1m + 2m2 + 4m2 = 40m + -4m2 + -40m + 4m2

Combine like terms: 2m2 + 4m2 = 6m2
-2 + -1m + 6m2 = 40m + -4m2 + -40m + 4m2

Reorder the terms:
-2 + -1m + 6m2 = 40m + -40m + -4m2 + 4m2

Combine like terms: 40m + -40m = 0
-2 + -1m + 6m2 = 0 + -4m2 + 4m2
-2 + -1m + 6m2 = -4m2 + 4m2

Combine like terms: -4m2 + 4m2 = 0
-2 + -1m + 6m2 = 0

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

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

Simplifying
-1 + -2m = 0

Solving
-1 + -2m = 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 + -2m = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2m = 0 + 1
-2m = 0 + 1

Combine like terms: 0 + 1 = 1
-2m = 1

Divide each side by '-2'.
m = -0.5

Simplifying
m = -0.5
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 = {-0.5, 0.6666666667}