2(5h-9)3h=8

Solution for 2(5h-9)3h=8 equation:

Simplifying
2(5h + -9) * 3h = 8

Reorder the terms:
2(-9 + 5h) * 3h = 8

Reorder the terms for easier multiplication:
2 * 3h(-9 + 5h) = 8

Multiply 2 * 3
6h(-9 + 5h) = 8
(-9 * 6h + 5h * 6h) = 8
(-54h + 30h2) = 8

Solving
-54h + 30h2 = 8

Solving for variable 'h'.

Reorder the terms:
-8 + -54h + 30h2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + -54h + 30h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-4 + -27h + 15h2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-4 + -27h + 15h2)' equal to zero and attempt to solve:

Simplifying
-4 + -27h + 15h2 = 0

Solving
-4 + -27h + 15h2 = 0

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

Divide each side by '15'.
-0.2666666667 + -1.8h + h2 = 0

Move the constant term to the right:

Add '0.2666666667' to each side of the equation.
-0.2666666667 + -1.8h + 0.2666666667 + h2 = 0 + 0.2666666667

Reorder the terms:
-0.2666666667 + 0.2666666667 + -1.8h + h2 = 0 + 0.2666666667

Combine like terms: -0.2666666667 + 0.2666666667 = 0.0000000000
0.0000000000 + -1.8h + h2 = 0 + 0.2666666667
-1.8h + h2 = 0 + 0.2666666667

Combine like terms: 0 + 0.2666666667 = 0.2666666667
-1.8h + h2 = 0.2666666667

The h term is -1.8h.  Take half its coefficient (-0.9).
Square it (0.81) and add it to both sides.

Add '0.81' to each side of the equation.
-1.8h + 0.81 + h2 = 0.2666666667 + 0.81

Reorder the terms:
0.81 + -1.8h + h2 = 0.2666666667 + 0.81

Combine like terms: 0.2666666667 + 0.81 = 1.0766666667
0.81 + -1.8h + h2 = 1.0766666667

Factor a perfect square on the left side:
(h + -0.9)(h + -0.9) = 1.0766666667

Calculate the square root of the right side: 1.037625494

Break this problem into two subproblems by setting 
(h + -0.9) equal to 1.037625494 and -1.037625494.

Subproblem 1
h + -0.9 = 1.037625494

Simplifying
h + -0.9 = 1.037625494

Reorder the terms:
-0.9 + h = 1.037625494

Solving
-0.9 + h = 1.037625494

Solving for variable 'h'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + h = 1.037625494 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + h = 1.037625494 + 0.9
h = 1.037625494 + 0.9

Combine like terms: 1.037625494 + 0.9 = 1.937625494
h = 1.937625494

Simplifying
h = 1.937625494

Subproblem 2
h + -0.9 = -1.037625494

Simplifying
h + -0.9 = -1.037625494

Reorder the terms:
-0.9 + h = -1.037625494

Solving
-0.9 + h = -1.037625494

Solving for variable 'h'.

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

Add '0.9' to each side of the equation.
-0.9 + 0.9 + h = -1.037625494 + 0.9

Combine like terms: -0.9 + 0.9 = 0.0
0.0 + h = -1.037625494 + 0.9
h = -1.037625494 + 0.9

Combine like terms: -1.037625494 + 0.9 = -0.137625494
h = -0.137625494

Simplifying
h = -0.137625494

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.937625494, -0.137625494}
Solution
h = {1.937625494, -0.137625494}