2m^2=3-5m

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

Simplifying
2m2 = 3 + -5m

Solving
2m2 = 3 + -5m

Solving for variable 'm'.

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

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

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

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

Factor a trinomial.
(-3 + -1m)(1 + -2m) = 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 '(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
Solution
m = {-3, 0.5}