40=(2h+6)(h)

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Solution for 40=(2h+6)(h) equation: 


Simplifying
40 = (2h + 6)(h)

Reorder the terms:
40 = (6 + 2h)(h)

Reorder the terms for easier multiplication:
40 = h(6 + 2h)
40 = (6 * h + 2h * h)
40 = (6h + 2h2)

Solving
40 = 6h + 2h2

Solving for variable 'h'.

Reorder the terms:
40 + -6h + -2h2 = 6h + -6h + 2h2 + -2h2

Combine like terms: 6h + -6h = 0
40 + -6h + -2h2 = 0 + 2h2 + -2h2
40 + -6h + -2h2 = 2h2 + -2h2

Combine like terms: 2h2 + -2h2 = 0
40 + -6h + -2h2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + -3h + -1h2) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(20 + -3h + -1h2)' equal to zero and attempt to solve:

Simplifying
20 + -3h + -1h2 = 0

Solving
20 + -3h + -1h2 = 0

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

Divide each side by '-1'.
-20 + 3h + h2 = 0

Move the constant term to the right:

Add '20' to each side of the equation.
-20 + 3h + 20 + h2 = 0 + 20

Reorder the terms:
-20 + 20 + 3h + h2 = 0 + 20

Combine like terms: -20 + 20 = 0
0 + 3h + h2 = 0 + 20
3h + h2 = 0 + 20

Combine like terms: 0 + 20 = 20
3h + h2 = 20

The h term is 3h.  Take half its coefficient (1.5).
Square it (2.25) and add it to both sides.

Add '2.25' to each side of the equation.
3h + 2.25 + h2 = 20 + 2.25

Reorder the terms:
2.25 + 3h + h2 = 20 + 2.25

Combine like terms: 20 + 2.25 = 22.25
2.25 + 3h + h2 = 22.25

Factor a perfect square on the left side:
(h + 1.5)(h + 1.5) = 22.25

Calculate the square root of the right side: 4.716990566

Break this problem into two subproblems by setting 
(h + 1.5) equal to 4.716990566 and -4.716990566.


Subproblem 1
h + 1.5 = 4.716990566

Simplifying
h + 1.5 = 4.716990566

Reorder the terms:
1.5 + h = 4.716990566

Solving
1.5 + h = 4.716990566

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = 4.716990566 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = 4.716990566 + -1.5
h = 4.716990566 + -1.5

Combine like terms: 4.716990566 + -1.5 = 3.216990566
h = 3.216990566

Simplifying
h = 3.216990566


Subproblem 2
h + 1.5 = -4.716990566

Simplifying
h + 1.5 = -4.716990566

Reorder the terms:
1.5 + h = -4.716990566

Solving
1.5 + h = -4.716990566

Solving for variable 'h'.

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

Add '-1.5' to each side of the equation.
1.5 + -1.5 + h = -4.716990566 + -1.5

Combine like terms: 1.5 + -1.5 = 0.0
0.0 + h = -4.716990566 + -1.5
h = -4.716990566 + -1.5

Combine like terms: -4.716990566 + -1.5 = -6.216990566
h = -6.216990566

Simplifying
h = -6.216990566


Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {3.216990566, -6.216990566}
Solution
h = {3.216990566, -6.216990566}

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