x^2(x+10)(x-2)=0

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Solution for x^2(x+10)(x-2)=0 equation: 


Simplifying
x2(x + 10)(x + -2) = 0

Reorder the terms:
x2(10 + x)(x + -2) = 0

Reorder the terms:
x2(10 + x)(-2 + x) = 0

Multiply (10 + x) * (-2 + x)
x2(10(-2 + x) + x(-2 + x)) = 0
x2((-2 * 10 + x * 10) + x(-2 + x)) = 0
x2((-20 + 10x) + x(-2 + x)) = 0
x2(-20 + 10x + (-2 * x + x * x)) = 0
x2(-20 + 10x + (-2x + x2)) = 0

Combine like terms: 10x + -2x = 8x
x2(-20 + 8x + x2) = 0
(-20 * x2 + 8x * x2 + x2 * x2) = 0
(-20x2 + 8x3 + x4) = 0

Solving
-20x2 + 8x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-20 + 8x + x2) = 0

Factor a trinomial.
x2((-10 + -1x)(2 + -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 '(-10 + -1x)' equal to zero and attempt to solve:

Simplifying
-10 + -1x = 0

Solving
-10 + -1x = 0

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

Add '10' to each side of the equation.
-10 + 10 + -1x = 0 + 10

Combine like terms: -10 + 10 = 0
0 + -1x = 0 + 10
-1x = 0 + 10

Combine like terms: 0 + 10 = 10
-1x = 10

Divide each side by '-1'.
x = -10

Simplifying
x = -10

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, -10, 2}

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