4m^2=-3m+1

Solution for 4m^2=-3m+1 equation:

Simplifying
4m2 = -3m + 1

Reorder the terms:
4m2 = 1 + -3m

Solving
4m2 = 1 + -3m

Solving for variable 'm'.

Reorder the terms:
-1 + 3m + 4m2 = 1 + -3m + -1 + 3m

Reorder the terms:
-1 + 3m + 4m2 = 1 + -1 + -3m + 3m

Combine like terms: 1 + -1 = 0
-1 + 3m + 4m2 = 0 + -3m + 3m
-1 + 3m + 4m2 = -3m + 3m

Combine like terms: -3m + 3m = 0
-1 + 3m + 4m2 = 0

Factor a trinomial.
(-1 + -1m)(1 + -4m) = 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 '(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
Solution
m = {-1, 0.25}