-h^2-5h+1=-10h^2+h+2

Solution for -h^2-5h+1=-10h^2+h+2 equation:

Simplifying
-1h2 + -5h + 1 = -10h2 + h + 2

Reorder the terms:
1 + -5h + -1h2 = -10h2 + h + 2

Reorder the terms:
1 + -5h + -1h2 = 2 + h + -10h2

Solving
1 + -5h + -1h2 = 2 + h + -10h2

Solving for variable 'h'.

Reorder the terms:
1 + -2 + -5h + -1h + -1h2 + 10h2 = 2 + h + -10h2 + -2 + -1h + 10h2

Combine like terms: 1 + -2 = -1
-1 + -5h + -1h + -1h2 + 10h2 = 2 + h + -10h2 + -2 + -1h + 10h2

Combine like terms: -5h + -1h = -6h
-1 + -6h + -1h2 + 10h2 = 2 + h + -10h2 + -2 + -1h + 10h2

Combine like terms: -1h2 + 10h2 = 9h2
-1 + -6h + 9h2 = 2 + h + -10h2 + -2 + -1h + 10h2

Reorder the terms:
-1 + -6h + 9h2 = 2 + -2 + h + -1h + -10h2 + 10h2

Combine like terms: 2 + -2 = 0
-1 + -6h + 9h2 = 0 + h + -1h + -10h2 + 10h2
-1 + -6h + 9h2 = h + -1h + -10h2 + 10h2

Combine like terms: h + -1h = 0
-1 + -6h + 9h2 = 0 + -10h2 + 10h2
-1 + -6h + 9h2 = -10h2 + 10h2

Combine like terms: -10h2 + 10h2 = 0
-1 + -6h + 9h2 = 0

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

Divide each side by '9'.
-0.1111111111 + -0.6666666667h + h2 = 0

Move the constant term to the right:

Add '0.1111111111' to each side of the equation.
-0.1111111111 + -0.6666666667h + 0.1111111111 + h2 = 0 + 0.1111111111

Reorder the terms:
-0.1111111111 + 0.1111111111 + -0.6666666667h + h2 = 0 + 0.1111111111

Combine like terms: -0.1111111111 + 0.1111111111 = 0.0000000000
0.0000000000 + -0.6666666667h + h2 = 0 + 0.1111111111
-0.6666666667h + h2 = 0 + 0.1111111111

Combine like terms: 0 + 0.1111111111 = 0.1111111111
-0.6666666667h + h2 = 0.1111111111

The h term is -0.6666666667h.  Take half its coefficient (-0.3333333334).
Square it (0.1111111112) and add it to both sides.

Add '0.1111111112' to each side of the equation.
-0.6666666667h + 0.1111111112 + h2 = 0.1111111111 + 0.1111111112

Reorder the terms:
0.1111111112 + -0.6666666667h + h2 = 0.1111111111 + 0.1111111112

Combine like terms: 0.1111111111 + 0.1111111112 = 0.2222222223
0.1111111112 + -0.6666666667h + h2 = 0.2222222223

Factor a perfect square on the left side:
(h + -0.3333333334)(h + -0.3333333334) = 0.2222222223

Calculate the square root of the right side: 0.471404521

Break this problem into two subproblems by setting 
(h + -0.3333333334) equal to 0.471404521 and -0.471404521.

Subproblem 1
h + -0.3333333334 = 0.471404521

Simplifying
h + -0.3333333334 = 0.471404521

Reorder the terms:
-0.3333333334 + h = 0.471404521

Solving
-0.3333333334 + h = 0.471404521

Solving for variable 'h'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + h = 0.471404521 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + h = 0.471404521 + 0.3333333334
h = 0.471404521 + 0.3333333334

Combine like terms: 0.471404521 + 0.3333333334 = 0.8047378544
h = 0.8047378544

Simplifying
h = 0.8047378544

Subproblem 2
h + -0.3333333334 = -0.471404521

Simplifying
h + -0.3333333334 = -0.471404521

Reorder the terms:
-0.3333333334 + h = -0.471404521

Solving
-0.3333333334 + h = -0.471404521

Solving for variable 'h'.

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

Add '0.3333333334' to each side of the equation.
-0.3333333334 + 0.3333333334 + h = -0.471404521 + 0.3333333334

Combine like terms: -0.3333333334 + 0.3333333334 = 0.0000000000
0.0000000000 + h = -0.471404521 + 0.3333333334
h = -0.471404521 + 0.3333333334

Combine like terms: -0.471404521 + 0.3333333334 = -0.1380711876
h = -0.1380711876

Simplifying
h = -0.1380711876

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.8047378544, -0.1380711876}