X^2(x+2)(x+6)=0

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Solution for X^2(x+2)(x+6)=0 equation: 


Simplifying
X2(x + 2)(x + 6) = 0

Reorder the terms:
X2(2 + x)(x + 6) = 0

Reorder the terms:
X2(2 + x)(6 + x) = 0

Multiply (2 + x) * (6 + x)
X2(2(6 + x) + x(6 + x)) = 0
X2((6 * 2 + x * 2) + x(6 + x)) = 0
X2((12 + 2x) + x(6 + x)) = 0
X2(12 + 2x + (6 * x + x * x)) = 0
X2(12 + 2x + (6x + x2)) = 0

Combine like terms: 2x + 6x = 8x
X2(12 + 8x + x2) = 0
(12 * X2 + 8x * X2 + x2 * X2) = 0
(12X2 + 8xX2 + x2X2) = 0

Solving
12X2 + 8xX2 + x2X2 = 0

Solving for variable 'X'.

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

Factor out the Greatest Common Factor (GCF), 'X2'.
X2(12 + 8x + x2) = 0

Factor a trinomial.
X2((6 + x)(2 + x)) = 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 '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Add '-1x' to each side of the equation.
x + -1x = -6 + -1x

Combine like terms: x + -1x = 0
0 = -6 + -1x

Simplifying
0 = -6 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

Subproblem 3
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 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 + x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + x = 0 + -2
x = 0 + -2

Combine like terms: 0 + -2 = -2
x = -2

Add '-1x' to each side of the equation.
x + -1x = -2 + -1x

Combine like terms: x + -1x = 0
0 = -2 + -1x

Simplifying
0 = -2 + -1x

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
X = {0}

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