3=7h(h-2)+17

Solution for 3=7h(h-2)+17 equation:

Simplifying
3 = 7h(h + -2) + 17

Reorder the terms:
3 = 7h(-2 + h) + 17
3 = (-2 * 7h + h * 7h) + 17
3 = (-14h + 7h2) + 17

Reorder the terms:
3 = 17 + -14h + 7h2

Solving
3 = 17 + -14h + 7h2

Solving for variable 'h'.

Combine like terms: 3 + -17 = -14
-14 + 14h + -7h2 = 17 + -14h + 7h2 + -17 + 14h + -7h2

Reorder the terms:
-14 + 14h + -7h2 = 17 + -17 + -14h + 14h + 7h2 + -7h2

Combine like terms: 17 + -17 = 0
-14 + 14h + -7h2 = 0 + -14h + 14h + 7h2 + -7h2
-14 + 14h + -7h2 = -14h + 14h + 7h2 + -7h2

Combine like terms: -14h + 14h = 0
-14 + 14h + -7h2 = 0 + 7h2 + -7h2
-14 + 14h + -7h2 = 7h2 + -7h2

Combine like terms: 7h2 + -7h2 = 0
-14 + 14h + -7h2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(-2 + 2h + -1h2) = 0

Ignore the factor 7.
Subproblem 1
Set the factor '(-2 + 2h + -1h2)' equal to zero and attempt to solve:

Simplifying
-2 + 2h + -1h2 = 0

Solving
-2 + 2h + -1h2 = 0

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

Divide each side by '-1'.
2 + -2h + h2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -2h + -2 + h2 = 0 + -2

Reorder the terms:
2 + -2 + -2h + h2 = 0 + -2

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

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

The h term is -2h.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2h + 1 + h2 = -2 + 1

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

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

Factor a perfect square on the left side:
(h + -1)(h + -1) = -1

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.