7h(h+2)+7=3(h+9)+2h

Solution for 7h(h+2)+7=3(h+9)+2h equation:

Simplifying
7h(h + 2) + 7 = 3(h + 9) + 2h

Reorder the terms:
7h(2 + h) + 7 = 3(h + 9) + 2h
(2 * 7h + h * 7h) + 7 = 3(h + 9) + 2h
(14h + 7h2) + 7 = 3(h + 9) + 2h

Reorder the terms:
7 + 14h + 7h2 = 3(h + 9) + 2h

Reorder the terms:
7 + 14h + 7h2 = 3(9 + h) + 2h
7 + 14h + 7h2 = (9 * 3 + h * 3) + 2h
7 + 14h + 7h2 = (27 + 3h) + 2h

Combine like terms: 3h + 2h = 5h
7 + 14h + 7h2 = 27 + 5h

Solving
7 + 14h + 7h2 = 27 + 5h

Solving for variable 'h'.

Reorder the terms:
7 + -27 + 14h + -5h + 7h2 = 27 + 5h + -27 + -5h

Combine like terms: 7 + -27 = -20
-20 + 14h + -5h + 7h2 = 27 + 5h + -27 + -5h

Combine like terms: 14h + -5h = 9h
-20 + 9h + 7h2 = 27 + 5h + -27 + -5h

Reorder the terms:
-20 + 9h + 7h2 = 27 + -27 + 5h + -5h

Combine like terms: 27 + -27 = 0
-20 + 9h + 7h2 = 0 + 5h + -5h
-20 + 9h + 7h2 = 5h + -5h

Combine like terms: 5h + -5h = 0
-20 + 9h + 7h2 = 0

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

Divide each side by '7'.
-2.857142857 + 1.285714286h + h2 = 0

Move the constant term to the right:

Add '2.857142857' to each side of the equation.
-2.857142857 + 1.285714286h + 2.857142857 + h2 = 0 + 2.857142857

Reorder the terms:
-2.857142857 + 2.857142857 + 1.285714286h + h2 = 0 + 2.857142857

Combine like terms: -2.857142857 + 2.857142857 = 0.000000000
0.000000000 + 1.285714286h + h2 = 0 + 2.857142857
1.285714286h + h2 = 0 + 2.857142857

Combine like terms: 0 + 2.857142857 = 2.857142857
1.285714286h + h2 = 2.857142857

The h term is 1.285714286h.  Take half its coefficient (0.642857143).
Square it (0.4132653063) and add it to both sides.

Add '0.4132653063' to each side of the equation.
1.285714286h + 0.4132653063 + h2 = 2.857142857 + 0.4132653063

Reorder the terms:
0.4132653063 + 1.285714286h + h2 = 2.857142857 + 0.4132653063

Combine like terms: 2.857142857 + 0.4132653063 = 3.2704081633
0.4132653063 + 1.285714286h + h2 = 3.2704081633

Factor a perfect square on the left side:
(h + 0.642857143)(h + 0.642857143) = 3.2704081633

Calculate the square root of the right side: 1.808426986

Break this problem into two subproblems by setting 
(h + 0.642857143) equal to 1.808426986 and -1.808426986.

Subproblem 1
h + 0.642857143 = 1.808426986

Simplifying
h + 0.642857143 = 1.808426986

Reorder the terms:
0.642857143 + h = 1.808426986

Solving
0.642857143 + h = 1.808426986

Solving for variable 'h'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + h = 1.808426986 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + h = 1.808426986 + -0.642857143
h = 1.808426986 + -0.642857143

Combine like terms: 1.808426986 + -0.642857143 = 1.165569843
h = 1.165569843

Simplifying
h = 1.165569843

Subproblem 2
h + 0.642857143 = -1.808426986

Simplifying
h + 0.642857143 = -1.808426986

Reorder the terms:
0.642857143 + h = -1.808426986

Solving
0.642857143 + h = -1.808426986

Solving for variable 'h'.

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

Add '-0.642857143' to each side of the equation.
0.642857143 + -0.642857143 + h = -1.808426986 + -0.642857143

Combine like terms: 0.642857143 + -0.642857143 = 0.000000000
0.000000000 + h = -1.808426986 + -0.642857143
h = -1.808426986 + -0.642857143

Combine like terms: -1.808426986 + -0.642857143 = -2.451284129
h = -2.451284129

Simplifying
h = -2.451284129

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {1.165569843, -2.451284129}