48h^2-12h=6

Solution for 48h^2-12h=6 equation:

Simplifying
48h2 + -12h = 6

Reorder the terms:
-12h + 48h2 = 6

Solving
-12h + 48h2 = 6

Solving for variable 'h'.

Reorder the terms:
-6 + -12h + 48h2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + -12h + 48h2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + -2h + 8h2) = 0

Factor a trinomial.
6((-1 + -4h)(1 + -2h)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -4h)' equal to zero and attempt to solve:

Simplifying
-1 + -4h = 0

Solving
-1 + -4h = 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 + -4h = 0 + 1

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

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

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

Simplifying
h = -0.25
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 = {-0.25, 0.5}