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

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


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

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

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

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

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

Solving
10x + -7x2 + x3 = 0

Solving for variable 'x'.

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

Factor a trinomial.
x((2 + -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 '(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 '(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, 2, 5}

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