-2m^2+3m=1

Solution for -2m^2+3m=1 equation:

Simplifying
-2m2 + 3m = 1

Reorder the terms:
3m + -2m2 = 1

Solving
3m + -2m2 = 1

Solving for variable 'm'.

Reorder the terms:
-1 + 3m + -2m2 = 1 + -1

Combine like terms: 1 + -1 = 0
-1 + 3m + -2m2 = 0

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

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

Simplifying
-1 + m = 0

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

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

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

Simplifying
m = 1
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 = {1, 0.5}