9h^2+3h-171=

Solution for 9h^2+3h-171= equation:

Simplifying
9h2 + 3h + -171 = 0

Reorder the terms:
-171 + 3h + 9h2 = 0

Solving
-171 + 3h + 9h2 = 0

Solving for variable 'h'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-57 + h + 3h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(-57 + h + 3h2)' equal to zero and attempt to solve:

Simplifying
-57 + h + 3h2 = 0

Solving
-57 + h + 3h2 = 0

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

Divide each side by '3'.
-19 + 0.3333333333h + h2 = 0

Move the constant term to the right:

Add '19' to each side of the equation.
-19 + 0.3333333333h + 19 + h2 = 0 + 19

Reorder the terms:
-19 + 19 + 0.3333333333h + h2 = 0 + 19

Combine like terms: -19 + 19 = 0
0 + 0.3333333333h + h2 = 0 + 19
0.3333333333h + h2 = 0 + 19

Combine like terms: 0 + 19 = 19
0.3333333333h + h2 = 19

The h term is h.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
0.3333333333h + 0.25 + h2 = 19 + 0.25

Reorder the terms:
0.25 + 0.3333333333h + h2 = 19 + 0.25

Combine like terms: 19 + 0.25 = 19.25
0.25 + 0.3333333333h + h2 = 19.25

Factor a perfect square on the left side:
(h + 0.5)(h + 0.5) = 19.25

Calculate the square root of the right side: 4.387482194

Break this problem into two subproblems by setting 
(h + 0.5) equal to 4.387482194 and -4.387482194.

Subproblem 1
h + 0.5 = 4.387482194

Simplifying
h + 0.5 = 4.387482194

Reorder the terms:
0.5 + h = 4.387482194

Solving
0.5 + h = 4.387482194

Solving for variable 'h'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + h = 4.387482194 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + h = 4.387482194 + -0.5
h = 4.387482194 + -0.5

Combine like terms: 4.387482194 + -0.5 = 3.887482194
h = 3.887482194

Simplifying
h = 3.887482194

Subproblem 2
h + 0.5 = -4.387482194

Simplifying
h + 0.5 = -4.387482194

Reorder the terms:
0.5 + h = -4.387482194

Solving
0.5 + h = -4.387482194

Solving for variable 'h'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + h = -4.387482194 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + h = -4.387482194 + -0.5
h = -4.387482194 + -0.5

Combine like terms: -4.387482194 + -0.5 = -4.887482194
h = -4.887482194

Simplifying
h = -4.887482194

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {3.887482194, -4.887482194}
Solution
h = {3.887482194, -4.887482194}