x^2(x+4)(x-2)=0

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Solution for x^2(x+4)(x-2)=0 equation:


Simplifying
x2(x + 4)(x + -2) = 0

Reorder the terms:
x2(4 + x)(x + -2) = 0

Reorder the terms:
x2(4 + x)(-2 + x) = 0

Multiply (4 + x) * (-2 + x)
x2(4(-2 + x) + x(-2 + x)) = 0
x2((-2 * 4 + x * 4) + x(-2 + x)) = 0
x2((-8 + 4x) + x(-2 + x)) = 0
x2(-8 + 4x + (-2 * x + x * x)) = 0
x2(-8 + 4x + (-2x + x2)) = 0

Combine like terms: 4x + -2x = 2x
x2(-8 + 2x + x2) = 0
(-8 * x2 + 2x * x2 + x2 * x2) = 0
(-8x2 + 2x3 + x4) = 0

Solving
-8x2 + 2x3 + x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x2'.
x2(-8 + 2x + x2) = 0

Factor a trinomial.
x2((-4 + -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 '(-4 + -1x)' equal to zero and attempt to solve:

Simplifying
-4 + -1x = 0

Solving
-4 + -1x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -1x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1x = 0 + 4
-1x = 0 + 4

Combine like terms: 0 + 4 = 4
-1x = 4

Divide each side by '-1'.
x = -4

Simplifying
x = -4

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, -4, 2}

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