x(x-4)(x-5)=0

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Solution for x(x-4)(x-5)=0 equation: 


Simplifying
x(x + -4)(x + -5) = 0

Reorder the terms:
x(-4 + x)(x + -5) = 0

Reorder the terms:
x(-4 + x)(-5 + x) = 0

Multiply (-4 + x) * (-5 + x)
x(-4(-5 + x) + x(-5 + x)) = 0
x((-5 * -4 + x * -4) + x(-5 + x)) = 0
x((20 + -4x) + x(-5 + x)) = 0
x(20 + -4x + (-5 * x + x * x)) = 0
x(20 + -4x + (-5x + x2)) = 0

Combine like terms: -4x + -5x = -9x
x(20 + -9x + x2) = 0
(20 * x + -9x * x + x2 * x) = 0
(20x + -9x2 + x3) = 0

Solving
20x + -9x2 + x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(20 + -9x + x2) = 0

Factor a trinomial.
x((4 + -1x)(5 + -1x)) = 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 '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 3
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {0, 4, 5}

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