24h^2-24h+6=0

Solution for 24h^2-24h+6=0 equation:

Simplifying
24h2 + -24h + 6 = 0

Reorder the terms:
6 + -24h + 24h2 = 0

Solving
6 + -24h + 24h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '6'.
6(1 + -4h + 4h2) = 0

Factor a trinomial.
6((1 + -2h)(1 + -2h)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(1 + -2h)' equal to zero and attempt to solve:

Simplifying
1 + -2h = 0

Solving
1 + -2h = 0

Move all terms containing h to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2h = 0 + -1
-2h = 0 + -1

Combine like terms: 0 + -1 = -1
-2h = -1

Divide each side by '-2'.
h = 0.5

Simplifying
h = 0.5
Subproblem 2
Set the factor '(1 + -2h)' equal to zero and attempt to solve:

Simplifying
1 + -2h = 0

Solving
1 + -2h = 0

Move all terms containing h to the left, all other terms to the right.

Add '-1' to each side of the equation.
1 + -1 + -2h = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2h = 0 + -1
-2h = 0 + -1

Combine like terms: 0 + -1 = -1
-2h = -1

Divide each side by '-2'.
h = 0.5

Simplifying
h = 0.5
Solution
h = {0.5, 0.5}