4h^2+12h=6

Solution for 4h^2+12h=6 equation:

Simplifying
4h2 + 12h = 6

Reorder the terms:
12h + 4h2 = 6

Solving
12h + 4h2 = 6

Solving for variable 'h'.

Reorder the terms:
-6 + 12h + 4h2 = 6 + -6

Combine like terms: 6 + -6 = 0
-6 + 12h + 4h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 6h + 2h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-3 + 6h + 2h2)' equal to zero and attempt to solve:

Simplifying
-3 + 6h + 2h2 = 0

Solving
-3 + 6h + 2h2 = 0

Begin completing the square.  Divide all terms by
2 the coefficient of the squared term: 

Divide each side by '2'.
-1.5 + 3h + h2 = 0

Move the constant term to the right:

Add '1.5' to each side of the equation.
-1.5 + 3h + 1.5 + h2 = 0 + 1.5

Reorder the terms:
-1.5 + 1.5 + 3h + h2 = 0 + 1.5

Combine like terms: -1.5 + 1.5 = 0.0
0.0 + 3h + h2 = 0 + 1.5
3h + h2 = 0 + 1.5

Combine like terms: 0 + 1.5 = 1.5
3h + h2 = 1.5

The h term is 3h.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3h + 2.25 + h2 = 1.5 + 2.25

Reorder the terms:
2.25 + 3h + h2 = 1.5 + 2.25

Combine like terms: 1.5 + 2.25 = 3.75
2.25 + 3h + h2 = 3.75

Factor a perfect square on the left side:
(h + 1.5)(h + 1.5) = 3.75

Calculate the square root of the right side: 1.936491673

Break this problem into two subproblems by setting 
(h + 1.5) equal to 1.936491673 and -1.936491673.

Subproblem 1
h + 1.5 = 1.936491673

Simplifying
h + 1.5 = 1.936491673

Reorder the terms:
1.5 + h = 1.936491673

Solving
1.5 + h = 1.936491673

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = 1.936491673 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = 1.936491673 + -1.5
h = 1.936491673 + -1.5

Combine like terms: 1.936491673 + -1.5 = 0.436491673
h = 0.436491673

Simplifying
h = 0.436491673

Subproblem 2
h + 1.5 = -1.936491673

Simplifying
h + 1.5 = -1.936491673

Reorder the terms:
1.5 + h = -1.936491673

Solving
1.5 + h = -1.936491673

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = -1.936491673 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = -1.936491673 + -1.5
h = -1.936491673 + -1.5

Combine like terms: -1.936491673 + -1.5 = -3.436491673
h = -3.436491673

Simplifying
h = -3.436491673

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.436491673, -3.436491673}
Solution
h = {0.436491673, -3.436491673}