2m^2-3m=5

Solution for 2m^2-3m=5 equation:

Simplifying
2m2 + -3m = 5

Reorder the terms:
-3m + 2m2 = 5

Solving
-3m + 2m2 = 5

Solving for variable 'm'.

Reorder the terms:
-5 + -3m + 2m2 = 5 + -5

Combine like terms: 5 + -5 = 0
-5 + -3m + 2m2 = 0

Factor a trinomial.
(-1 + -1m)(5 + -2m) = 0

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

Simplifying
-1 + -1m = 0

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

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

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

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

Simplifying
m = -1
Subproblem 2
Set the factor '(5 + -2m)' equal to zero and attempt to solve:

Simplifying
5 + -2m = 0

Solving
5 + -2m = 0

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

Add '-5' to each side of the equation.
5 + -5 + -2m = 0 + -5

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

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

Divide each side by '-2'.
m = 2.5

Simplifying
m = 2.5
Solution
m = {-1, 2.5}