-4m^2+14m-6=0

Solution for -4m^2+14m-6=0 equation:

Simplifying
-4m2 + 14m + -6 = 0

Reorder the terms:
-6 + 14m + -4m2 = 0

Solving
-6 + 14m + -4m2 = 0

Solving for variable 'm'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 7m + -2m2) = 0

Factor a trinomial.
2((-3 + m)(1 + -2m)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + m)' equal to zero and attempt to solve:

Simplifying
-3 + m = 0

Solving
-3 + m = 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 + m = 0 + 3

Combine like terms: -3 + 3 = 0
0 + m = 0 + 3
m = 0 + 3

Combine like terms: 0 + 3 = 3
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}