(h-7)(h-5)=2h+2(h+3)

Solution for (h-7)(h-5)=2h+2(h+3) equation:

Simplifying
(h + -7)(h + -5) = 2h + 2(h + 3)

Reorder the terms:
(-7 + h)(h + -5) = 2h + 2(h + 3)

Reorder the terms:
(-7 + h)(-5 + h) = 2h + 2(h + 3)

Multiply (-7 + h) * (-5 + h)
(-7(-5 + h) + h(-5 + h)) = 2h + 2(h + 3)
((-5 * -7 + h * -7) + h(-5 + h)) = 2h + 2(h + 3)
((35 + -7h) + h(-5 + h)) = 2h + 2(h + 3)
(35 + -7h + (-5 * h + h * h)) = 2h + 2(h + 3)
(35 + -7h + (-5h + h2)) = 2h + 2(h + 3)

Combine like terms: -7h + -5h = -12h
(35 + -12h + h2) = 2h + 2(h + 3)

Reorder the terms:
35 + -12h + h2 = 2h + 2(3 + h)
35 + -12h + h2 = 2h + (3 * 2 + h * 2)
35 + -12h + h2 = 2h + (6 + 2h)

Reorder the terms:
35 + -12h + h2 = 6 + 2h + 2h

Combine like terms: 2h + 2h = 4h
35 + -12h + h2 = 6 + 4h

Solving
35 + -12h + h2 = 6 + 4h

Solving for variable 'h'.

Reorder the terms:
35 + -6 + -12h + -4h + h2 = 6 + 4h + -6 + -4h

Combine like terms: 35 + -6 = 29
29 + -12h + -4h + h2 = 6 + 4h + -6 + -4h

Combine like terms: -12h + -4h = -16h
29 + -16h + h2 = 6 + 4h + -6 + -4h

Reorder the terms:
29 + -16h + h2 = 6 + -6 + 4h + -4h

Combine like terms: 6 + -6 = 0
29 + -16h + h2 = 0 + 4h + -4h
29 + -16h + h2 = 4h + -4h

Combine like terms: 4h + -4h = 0
29 + -16h + h2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-29' to each side of the equation.
29 + -16h + -29 + h2 = 0 + -29

Reorder the terms:
29 + -29 + -16h + h2 = 0 + -29

Combine like terms: 29 + -29 = 0
0 + -16h + h2 = 0 + -29
-16h + h2 = 0 + -29

Combine like terms: 0 + -29 = -29
-16h + h2 = -29

The h term is -16h.  Take half its coefficient (-8).
Square it (64) and add it to both sides.

Add '64' to each side of the equation.
-16h + 64 + h2 = -29 + 64

Reorder the terms:
64 + -16h + h2 = -29 + 64

Combine like terms: -29 + 64 = 35
64 + -16h + h2 = 35

Factor a perfect square on the left side:
(h + -8)(h + -8) = 35

Calculate the square root of the right side: 5.916079783

Break this problem into two subproblems by setting 
(h + -8) equal to 5.916079783 and -5.916079783.

Subproblem 1
h + -8 = 5.916079783

Simplifying
h + -8 = 5.916079783

Reorder the terms:
-8 + h = 5.916079783

Solving
-8 + h = 5.916079783

Solving for variable 'h'.

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

Add '8' to each side of the equation.
-8 + 8 + h = 5.916079783 + 8

Combine like terms: -8 + 8 = 0
0 + h = 5.916079783 + 8
h = 5.916079783 + 8

Combine like terms: 5.916079783 + 8 = 13.916079783
h = 13.916079783

Simplifying
h = 13.916079783

Subproblem 2
h + -8 = -5.916079783

Simplifying
h + -8 = -5.916079783

Reorder the terms:
-8 + h = -5.916079783

Solving
-8 + h = -5.916079783

Solving for variable 'h'.

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

Add '8' to each side of the equation.
-8 + 8 + h = -5.916079783 + 8

Combine like terms: -8 + 8 = 0
0 + h = -5.916079783 + 8
h = -5.916079783 + 8

Combine like terms: -5.916079783 + 8 = 2.083920217
h = 2.083920217

Simplifying
h = 2.083920217

Solution
The solution to the problem is based on the solutions
from the subproblems.
h = {13.916079783, 2.083920217}