(72-2h)(72-2h)(72-4x)=36x^2-2x^3

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Solution for (72-2h)(72-2h)(72-4x)=36x^2-2x^3 equation: 


Simplifying
(72 + -2h)(72 + -2h)(72 + -4x) = 36x2 + -2x3

Multiply (72 + -2h) * (72 + -2h)
(72(72 + -2h) + -2h * (72 + -2h))(72 + -4x) = 36x2 + -2x3
((72 * 72 + -2h * 72) + -2h * (72 + -2h))(72 + -4x) = 36x2 + -2x3
((5184 + -144h) + -2h * (72 + -2h))(72 + -4x) = 36x2 + -2x3
(5184 + -144h + (72 * -2h + -2h * -2h))(72 + -4x) = 36x2 + -2x3
(5184 + -144h + (-144h + 4h2))(72 + -4x) = 36x2 + -2x3

Combine like terms: -144h + -144h = -288h
(5184 + -288h + 4h2)(72 + -4x) = 36x2 + -2x3

Multiply (5184 + -288h + 4h2) * (72 + -4x)
(5184(72 + -4x) + -288h * (72 + -4x) + 4h2 * (72 + -4x)) = 36x2 + -2x3
((72 * 5184 + -4x * 5184) + -288h * (72 + -4x) + 4h2 * (72 + -4x)) = 36x2 + -2x3
((373248 + -20736x) + -288h * (72 + -4x) + 4h2 * (72 + -4x)) = 36x2 + -2x3
(373248 + -20736x + (72 * -288h + -4x * -288h) + 4h2 * (72 + -4x)) = 36x2 + -2x3
(373248 + -20736x + (-20736h + 1152hx) + 4h2 * (72 + -4x)) = 36x2 + -2x3
(373248 + -20736x + -20736h + 1152hx + (72 * 4h2 + -4x * 4h2)) = 36x2 + -2x3
(373248 + -20736x + -20736h + 1152hx + (288h2 + -16h2x)) = 36x2 + -2x3

Reorder the terms:
(373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x) = 36x2 + -2x3
(373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x) = 36x2 + -2x3

Solving
373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x = 36x2 + -2x3

Solving for variable 'h'.

Reorder the terms:
373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x + -36x2 + 2x3 = 36x2 + -36x2 + -2x3 + 2x3

Combine like terms: 36x2 + -36x2 = 0
373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x + -36x2 + 2x3 = 0 + -2x3 + 2x3
373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x + -36x2 + 2x3 = -2x3 + 2x3

Combine like terms: -2x3 + 2x3 = 0
373248 + -20736h + 1152hx + 288h2 + -16h2x + -20736x + -36x2 + 2x3 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(186624 + -10368h + 576hx + 144h2 + -8h2x + -10368x + -18x2 + x3) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(186624 + -10368h + 576hx + 144h2 + -8h2x + -10368x + -18x2 + x3)' equal to zero and attempt to solve:

Simplifying
186624 + -10368h + 576hx + 144h2 + -8h2x + -10368x + -18x2 + x3 = 0

Solving
186624 + -10368h + 576hx + 144h2 + -8h2x + -10368x + -18x2 + x3 = 0

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.

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