H(x)=x(x+2)(x-5)

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Solution for H(x)=x(x+2)(x-5) equation: 


Simplifying
H(x) = x(x + 2)(x + -5)

Multiply H * x
xH = x(x + 2)(x + -5)

Reorder the terms:
xH = x(2 + x)(x + -5)

Reorder the terms:
xH = x(2 + x)(-5 + x)

Multiply (2 + x) * (-5 + x)
xH = x(2(-5 + x) + x(-5 + x))
xH = x((-5 * 2 + x * 2) + x(-5 + x))
xH = x((-10 + 2x) + x(-5 + x))
xH = x(-10 + 2x + (-5 * x + x * x))
xH = x(-10 + 2x + (-5x + x2))

Combine like terms: 2x + -5x = -3x
xH = x(-10 + -3x + x2)
xH = (-10 * x + -3x * x + x2 * x)
xH = (-10x + -3x2 + x3)

Solving
xH = -10x + -3x2 + x3

Solving for variable 'x'.

Reorder the terms:
10x + xH + 3x2 + -1x3 = -10x + -3x2 + x3 + 10x + 3x2 + -1x3

Reorder the terms:
10x + xH + 3x2 + -1x3 = -10x + 10x + -3x2 + 3x2 + x3 + -1x3

Combine like terms: -10x + 10x = 0
10x + xH + 3x2 + -1x3 = 0 + -3x2 + 3x2 + x3 + -1x3
10x + xH + 3x2 + -1x3 = -3x2 + 3x2 + x3 + -1x3

Combine like terms: -3x2 + 3x2 = 0
10x + xH + 3x2 + -1x3 = 0 + x3 + -1x3
10x + xH + 3x2 + -1x3 = x3 + -1x3

Combine like terms: x3 + -1x3 = 0
10x + xH + 3x2 + -1x3 = 0

Factor out the Greatest Common Factor (GCF), 'x'.
x(10 + H + 3x + -1x2) = 0


Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(10 + H + 3x + -1x2)' equal to zero and attempt to solve:

Simplifying
10 + H + 3x + -1x2 = 0

Solving
10 + H + 3x + -1x2 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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