0.5h+0.33h(h-6)=0.833h+2

Solution for 0.5h+0.33h(h-6)=0.833h+2 equation:

Simplifying
0.5h + 0.33h(h + -6) = 0.833h + 2

Reorder the terms:
0.5h + 0.33h(-6 + h) = 0.833h + 2
0.5h + (-6 * 0.33h + h * 0.33h) = 0.833h + 2
0.5h + (-1.98h + 0.33h2) = 0.833h + 2

Combine like terms: 0.5h + -1.98h = -1.48h
-1.48h + 0.33h2 = 0.833h + 2

Reorder the terms:
-1.48h + 0.33h2 = 2 + 0.833h

Solving
-1.48h + 0.33h2 = 2 + 0.833h

Solving for variable 'h'.

Reorder the terms:
-2 + -1.48h + -0.833h + 0.33h2 = 2 + 0.833h + -2 + -0.833h

Combine like terms: -1.48h + -0.833h = -2.313h
-2 + -2.313h + 0.33h2 = 2 + 0.833h + -2 + -0.833h

Reorder the terms:
-2 + -2.313h + 0.33h2 = 2 + -2 + 0.833h + -0.833h

Combine like terms: 2 + -2 = 0
-2 + -2.313h + 0.33h2 = 0 + 0.833h + -0.833h
-2 + -2.313h + 0.33h2 = 0.833h + -0.833h

Combine like terms: 0.833h + -0.833h = 0.000
-2 + -2.313h + 0.33h2 = 0.000

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

Divide each side by '0.33'.
-6.060606061 + -7.009090909h + h2 = 0.0

Move the constant term to the right:

Add '6.060606061' to each side of the equation.
-6.060606061 + -7.009090909h + 6.060606061 + h2 = 0.0 + 6.060606061

Reorder the terms:
-6.060606061 + 6.060606061 + -7.009090909h + h2 = 0.0 + 6.060606061

Combine like terms: -6.060606061 + 6.060606061 = 0.000000000
0.000000000 + -7.009090909h + h2 = 0.0 + 6.060606061
-7.009090909h + h2 = 0.0 + 6.060606061

Combine like terms: 0.0 + 6.060606061 = 6.060606061
-7.009090909h + h2 = 6.060606061

The h term is -7.009090909h.  Take half its coefficient (-3.504545455).
Square it (12.28183885) and add it to both sides.

Add '12.28183885' to each side of the equation.
-7.009090909h + 12.28183885 + h2 = 6.060606061 + 12.28183885

Reorder the terms:
12.28183885 + -7.009090909h + h2 = 6.060606061 + 12.28183885

Combine like terms: 6.060606061 + 12.28183885 = 18.342444911
12.28183885 + -7.009090909h + h2 = 18.342444911

Factor a perfect square on the left side:
(h + -3.504545455)(h + -3.504545455) = 18.342444911

Calculate the square root of the right side: 4.282808064

Break this problem into two subproblems by setting 
(h + -3.504545455) equal to 4.282808064 and -4.282808064.

Subproblem 1
h + -3.504545455 = 4.282808064

Simplifying
h + -3.504545455 = 4.282808064

Reorder the terms:
-3.504545455 + h = 4.282808064

Solving
-3.504545455 + h = 4.282808064

Solving for variable 'h'.

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

Add '3.504545455' to each side of the equation.
-3.504545455 + 3.504545455 + h = 4.282808064 + 3.504545455

Combine like terms: -3.504545455 + 3.504545455 = 0.000000000
0.000000000 + h = 4.282808064 + 3.504545455
h = 4.282808064 + 3.504545455

Combine like terms: 4.282808064 + 3.504545455 = 7.787353519
h = 7.787353519

Simplifying
h = 7.787353519

Subproblem 2
h + -3.504545455 = -4.282808064

Simplifying
h + -3.504545455 = -4.282808064

Reorder the terms:
-3.504545455 + h = -4.282808064

Solving
-3.504545455 + h = -4.282808064

Solving for variable 'h'.

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

Add '3.504545455' to each side of the equation.
-3.504545455 + 3.504545455 + h = -4.282808064 + 3.504545455

Combine like terms: -3.504545455 + 3.504545455 = 0.000000000
0.000000000 + h = -4.282808064 + 3.504545455
h = -4.282808064 + 3.504545455

Combine like terms: -4.282808064 + 3.504545455 = -0.778262609
h = -0.778262609

Simplifying
h = -0.778262609

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {7.787353519, -0.778262609}