-3h(h+7)=-18

Solution for -3h(h+7)=-18 equation:

Simplifying
-3h(h + 7) = -18

Reorder the terms:
-3h(7 + h) = -18
(7 * -3h + h * -3h) = -18
(-21h + -3h2) = -18

Solving
-21h + -3h2 = -18

Solving for variable 'h'.

Reorder the terms:
18 + -21h + -3h2 = -18 + 18

Combine like terms: -18 + 18 = 0
18 + -21h + -3h2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(6 + -7h + -1h2) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(6 + -7h + -1h2)' equal to zero and attempt to solve:

Simplifying
6 + -7h + -1h2 = 0

Solving
6 + -7h + -1h2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
-6 + 7h + h2 = 0

Move the constant term to the right:

Add '6' to each side of the equation.
-6 + 7h + 6 + h2 = 0 + 6

Reorder the terms:
-6 + 6 + 7h + h2 = 0 + 6

Combine like terms: -6 + 6 = 0
0 + 7h + h2 = 0 + 6
7h + h2 = 0 + 6

Combine like terms: 0 + 6 = 6
7h + h2 = 6

The h term is 7h.  Take half its coefficient (3.5).
Square it (12.25) and add it to both sides.

Add '12.25' to each side of the equation.
7h + 12.25 + h2 = 6 + 12.25

Reorder the terms:
12.25 + 7h + h2 = 6 + 12.25

Combine like terms: 6 + 12.25 = 18.25
12.25 + 7h + h2 = 18.25

Factor a perfect square on the left side:
(h + 3.5)(h + 3.5) = 18.25

Calculate the square root of the right side: 4.272001873

Break this problem into two subproblems by setting 
(h + 3.5) equal to 4.272001873 and -4.272001873.

Subproblem 1
h + 3.5 = 4.272001873

Simplifying
h + 3.5 = 4.272001873

Reorder the terms:
3.5 + h = 4.272001873

Solving
3.5 + h = 4.272001873

Solving for variable 'h'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + h = 4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + h = 4.272001873 + -3.5
h = 4.272001873 + -3.5

Combine like terms: 4.272001873 + -3.5 = 0.772001873
h = 0.772001873

Simplifying
h = 0.772001873

Subproblem 2
h + 3.5 = -4.272001873

Simplifying
h + 3.5 = -4.272001873

Reorder the terms:
3.5 + h = -4.272001873

Solving
3.5 + h = -4.272001873

Solving for variable 'h'.

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

Add '-3.5' to each side of the equation.
3.5 + -3.5 + h = -4.272001873 + -3.5

Combine like terms: 3.5 + -3.5 = 0.0
0.0 + h = -4.272001873 + -3.5
h = -4.272001873 + -3.5

Combine like terms: -4.272001873 + -3.5 = -7.772001873
h = -7.772001873

Simplifying
h = -7.772001873

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {0.772001873, -7.772001873}
Solution
h = {0.772001873, -7.772001873}