2m^2=5m+3

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

Simplifying
2m2 = 5m + 3

Reorder the terms:
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.
(-1 + -2m)(3 + -1m) = 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 '(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
Solution
m = {-0.5, 3}