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

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


Simplifying
x(5 + -1x)(x + -2) = 0

Reorder the terms:
x(5 + -1x)(-2 + x) = 0

Multiply (5 + -1x) * (-2 + x)
x(5(-2 + x) + -1x * (-2 + x)) = 0
x((-2 * 5 + x * 5) + -1x * (-2 + x)) = 0
x((-10 + 5x) + -1x * (-2 + x)) = 0
x(-10 + 5x + (-2 * -1x + x * -1x)) = 0
x(-10 + 5x + (2x + -1x2)) = 0

Combine like terms: 5x + 2x = 7x
x(-10 + 7x + -1x2) = 0
(-10 * x + 7x * x + -1x2 * x) = 0
(-10x + 7x2 + -1x3) = 0

Solving
-10x + 7x2 + -1x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-10 + 7x + -1x2) = 0

Factor a trinomial.
x((-5 + x)(2 + -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 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 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 + x = 0 + 5

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

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

Simplifying
x = 5

Subproblem 3
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
Solution
x = {0, 5, 2}

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