0=-5x(x^2-36x)(x-2)

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Solution for 0=-5x(x^2-36x)(x-2) equation: 


Simplifying
0 = -5x(x2 + -36x)(x + -2)

Reorder the terms:
0 = -5x(-36x + x2)(x + -2)

Reorder the terms:
0 = -5x(-36x + x2)(-2 + x)

Multiply (-36x + x2) * (-2 + x)
0 = -5x(-36x * (-2 + x) + x2(-2 + x))
0 = -5x((-2 * -36x + x * -36x) + x2(-2 + x))
0 = -5x((72x + -36x2) + x2(-2 + x))
0 = -5x(72x + -36x2 + (-2 * x2 + x * x2))
0 = -5x(72x + -36x2 + (-2x2 + x3))

Combine like terms: -36x2 + -2x2 = -38x2
0 = -5x(72x + -38x2 + x3)
0 = (72x * -5x + -38x2 * -5x + x3 * -5x)
0 = (-360x2 + 190x3 + -5x4)

Solving
0 = -360x2 + 190x3 + -5x4

Solving for variable 'x'.
Remove the zero:
360x2 + -190x3 + 5x4 = -360x2 + 190x3 + -5x4 + 360x2 + -190x3 + 5x4

Reorder the terms:
360x2 + -190x3 + 5x4 = -360x2 + 360x2 + 190x3 + -190x3 + -5x4 + 5x4

Combine like terms: -360x2 + 360x2 = 0
360x2 + -190x3 + 5x4 = 0 + 190x3 + -190x3 + -5x4 + 5x4
360x2 + -190x3 + 5x4 = 190x3 + -190x3 + -5x4 + 5x4

Combine like terms: 190x3 + -190x3 = 0
360x2 + -190x3 + 5x4 = 0 + -5x4 + 5x4
360x2 + -190x3 + 5x4 = -5x4 + 5x4

Combine like terms: -5x4 + 5x4 = 0
360x2 + -190x3 + 5x4 = 0

Factor out the Greatest Common Factor (GCF), '5x2'.
5x2(72 + -38x + x2) = 0

Factor a trinomial.
5x2((2 + -1x)(36 + -1x)) = 0

Ignore the factor 5.

Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2

Subproblem 3
Set the factor '(36 + -1x)' equal to zero and attempt to solve:

Simplifying
36 + -1x = 0

Solving
36 + -1x = 0

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

Add '-36' to each side of the equation.
36 + -36 + -1x = 0 + -36

Combine like terms: 36 + -36 = 0
0 + -1x = 0 + -36
-1x = 0 + -36

Combine like terms: 0 + -36 = -36
-1x = -36

Divide each side by '-1'.
x = 36

Simplifying
x = 36
Solution
x = {0, 2, 36}

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