(5-x)*x*(8-x)=0

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Solution for (5-x)*x*(8-x)=0 equation:


Simplifying
(5 + -1x) * x(8 + -1x) = 0

Reorder the terms for easier multiplication:
x(5 + -1x)(8 + -1x) = 0

Multiply (5 + -1x) * (8 + -1x)
x(5(8 + -1x) + -1x * (8 + -1x)) = 0
x((8 * 5 + -1x * 5) + -1x * (8 + -1x)) = 0
x((40 + -5x) + -1x * (8 + -1x)) = 0
x(40 + -5x + (8 * -1x + -1x * -1x)) = 0
x(40 + -5x + (-8x + 1x2)) = 0

Combine like terms: -5x + -8x = -13x
x(40 + -13x + 1x2) = 0
(40 * x + -13x * x + 1x2 * x) = 0
(40x + -13x2 + 1x3) = 0

Solving
40x + -13x2 + 1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(40 + -13x + x2) = 0

Factor a trinomial.
x((5 + -1x)(8 + -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 '(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

Subproblem 3
Set the factor '(8 + -1x)' equal to zero and attempt to solve:

Simplifying
8 + -1x = 0

Solving
8 + -1x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
x = 8

Simplifying
x = 8
Solution
x = {0, 5, 8}

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