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

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


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

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

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

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

Combine like terms: -5x + -2x = -7x
x2(10 + -7x + x2) = 0
(10 * x2 + -7x * x2 + x2 * x2) = 0
(10x2 + -7x3 + x4) = 0

Solving
10x2 + -7x3 + x4 = 0

Solving for variable 'x'.

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

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


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 '(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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