-6h^2-7h+6=0

Solution for -6h^2-7h+6=0 equation:

Simplifying
-6h2 + -7h + 6 = 0

Reorder the terms:
6 + -7h + -6h2 = 0

Solving
6 + -7h + -6h2 = 0

Solving for variable 'h'.

Begin completing the square.  Divide all terms by
-6 the coefficient of the squared term: 

Divide each side by '-6'.
-1 + 1.166666667h + h2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 1.166666667h + 1 + h2 = 0 + 1

Reorder the terms:
-1 + 1 + 1.166666667h + h2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 1.166666667h + h2 = 0 + 1
1.166666667h + h2 = 0 + 1

Combine like terms: 0 + 1 = 1
1.166666667h + h2 = 1

The h term is 1.166666667h.  Take half its coefficient (0.5833333335).
Square it (0.3402777780) and add it to both sides.

Add '0.3402777780' to each side of the equation.
1.166666667h + 0.3402777780 + h2 = 1 + 0.3402777780

Reorder the terms:
0.3402777780 + 1.166666667h + h2 = 1 + 0.3402777780

Combine like terms: 1 + 0.3402777780 = 1.340277778
0.3402777780 + 1.166666667h + h2 = 1.340277778

Factor a perfect square on the left side:
(h + 0.5833333335)(h + 0.5833333335) = 1.340277778

Calculate the square root of the right side: 1.157703666

Break this problem into two subproblems by setting 
(h + 0.5833333335) equal to 1.157703666 and -1.157703666.

Subproblem 1
h + 0.5833333335 = 1.157703666

Simplifying
h + 0.5833333335 = 1.157703666

Reorder the terms:
0.5833333335 + h = 1.157703666

Solving
0.5833333335 + h = 1.157703666

Solving for variable 'h'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + h = 1.157703666 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + h = 1.157703666 + -0.5833333335
h = 1.157703666 + -0.5833333335

Combine like terms: 1.157703666 + -0.5833333335 = 0.5743703325
h = 0.5743703325

Simplifying
h = 0.5743703325

Subproblem 2
h + 0.5833333335 = -1.157703666

Simplifying
h + 0.5833333335 = -1.157703666

Reorder the terms:
0.5833333335 + h = -1.157703666

Solving
0.5833333335 + h = -1.157703666

Solving for variable 'h'.

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

Add '-0.5833333335' to each side of the equation.
0.5833333335 + -0.5833333335 + h = -1.157703666 + -0.5833333335

Combine like terms: 0.5833333335 + -0.5833333335 = 0.0000000000
0.0000000000 + h = -1.157703666 + -0.5833333335
h = -1.157703666 + -0.5833333335

Combine like terms: -1.157703666 + -0.5833333335 = -1.7410369995
h = -1.7410369995

Simplifying
h = -1.7410369995

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.5743703325, -1.7410369995}