4m^2=5m-1

Solution for 4m^2=5m-1 equation:

Simplifying
4m2 = 5m + -1

Reorder the terms:
4m2 = -1 + 5m

Solving
4m2 = -1 + 5m

Solving for variable 'm'.

Reorder the terms:
1 + -5m + 4m2 = -1 + 5m + 1 + -5m

Reorder the terms:
1 + -5m + 4m2 = -1 + 1 + 5m + -5m

Combine like terms: -1 + 1 = 0
1 + -5m + 4m2 = 0 + 5m + -5m
1 + -5m + 4m2 = 5m + -5m

Combine like terms: 5m + -5m = 0
1 + -5m + 4m2 = 0

Factor a trinomial.
(1 + -4m)(1 + -1m) = 0

Subproblem 1
Set the factor '(1 + -4m)' equal to zero and attempt to solve:

Simplifying
1 + -4m = 0

Solving
1 + -4m = 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 + -4m = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -4m = 0 + -1
-4m = 0 + -1

Combine like terms: 0 + -1 = -1
-4m = -1

Divide each side by '-4'.
m = 0.25

Simplifying
m = 0.25
Subproblem 2
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
Solution
m = {0.25, 1}