2h^2+4h+4=336

Solution for 2h^2+4h+4=336 equation:

Simplifying
2h2 + 4h + 4 = 336

Reorder the terms:
4 + 4h + 2h2 = 336

Solving
4 + 4h + 2h2 = 336

Solving for variable 'h'.

Reorder the terms:
4 + -336 + 4h + 2h2 = 336 + -336

Combine like terms: 4 + -336 = -332
-332 + 4h + 2h2 = 336 + -336

Combine like terms: 336 + -336 = 0
-332 + 4h + 2h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-166 + 2h + h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-166 + 2h + h2)' equal to zero and attempt to solve:

Simplifying
-166 + 2h + h2 = 0

Solving
-166 + 2h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '166' to each side of the equation.
-166 + 2h + 166 + h2 = 0 + 166

Reorder the terms:
-166 + 166 + 2h + h2 = 0 + 166

Combine like terms: -166 + 166 = 0
0 + 2h + h2 = 0 + 166
2h + h2 = 0 + 166

Combine like terms: 0 + 166 = 166
2h + h2 = 166

The h term is 2h.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2h + 1 + h2 = 166 + 1

Reorder the terms:
1 + 2h + h2 = 166 + 1

Combine like terms: 166 + 1 = 167
1 + 2h + h2 = 167

Factor a perfect square on the left side:
(h + 1)(h + 1) = 167

Calculate the square root of the right side: 12.922847983

Break this problem into two subproblems by setting 
(h + 1) equal to 12.922847983 and -12.922847983.

Subproblem 1
h + 1 = 12.922847983

Simplifying
h + 1 = 12.922847983

Reorder the terms:
1 + h = 12.922847983

Solving
1 + h = 12.922847983

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = 12.922847983 + -1

Combine like terms: 1 + -1 = 0
0 + h = 12.922847983 + -1
h = 12.922847983 + -1

Combine like terms: 12.922847983 + -1 = 11.922847983
h = 11.922847983

Simplifying
h = 11.922847983

Subproblem 2
h + 1 = -12.922847983

Simplifying
h + 1 = -12.922847983

Reorder the terms:
1 + h = -12.922847983

Solving
1 + h = -12.922847983

Solving for variable 'h'.

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

Add '-1' to each side of the equation.
1 + -1 + h = -12.922847983 + -1

Combine like terms: 1 + -1 = 0
0 + h = -12.922847983 + -1
h = -12.922847983 + -1

Combine like terms: -12.922847983 + -1 = -13.922847983
h = -13.922847983

Simplifying
h = -13.922847983

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {11.922847983, -13.922847983}
Solution
h = {11.922847983, -13.922847983}