(12-x^2)(x^2+6)(x^2-3x)=0

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Solution for (12-x^2)(x^2+6)(x^2-3x)=0 equation:


Simplifying
(12 + -1x2)(x2 + 6)(x2 + -3x) = 0

Reorder the terms:
(12 + -1x2)(6 + x2)(x2 + -3x) = 0

Reorder the terms:
(12 + -1x2)(6 + x2)(-3x + x2) = 0

Multiply (12 + -1x2) * (6 + x2)
(12(6 + x2) + -1x2 * (6 + x2))(-3x + x2) = 0
((6 * 12 + x2 * 12) + -1x2 * (6 + x2))(-3x + x2) = 0
((72 + 12x2) + -1x2 * (6 + x2))(-3x + x2) = 0
(72 + 12x2 + (6 * -1x2 + x2 * -1x2))(-3x + x2) = 0
(72 + 12x2 + (-6x2 + -1x4))(-3x + x2) = 0

Combine like terms: 12x2 + -6x2 = 6x2
(72 + 6x2 + -1x4)(-3x + x2) = 0

Multiply (72 + 6x2 + -1x4) * (-3x + x2)
(72(-3x + x2) + 6x2 * (-3x + x2) + -1x4 * (-3x + x2)) = 0
((-3x * 72 + x2 * 72) + 6x2 * (-3x + x2) + -1x4 * (-3x + x2)) = 0
((-216x + 72x2) + 6x2 * (-3x + x2) + -1x4 * (-3x + x2)) = 0
(-216x + 72x2 + (-3x * 6x2 + x2 * 6x2) + -1x4 * (-3x + x2)) = 0
(-216x + 72x2 + (-18x3 + 6x4) + -1x4 * (-3x + x2)) = 0
(-216x + 72x2 + -18x3 + 6x4 + (-3x * -1x4 + x2 * -1x4)) = 0
(-216x + 72x2 + -18x3 + 6x4 + (3x5 + -1x6)) = 0
(-216x + 72x2 + -18x3 + 6x4 + 3x5 + -1x6) = 0

Solving
-216x + 72x2 + -18x3 + 6x4 + 3x5 + -1x6 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(-216 + 72x + -18x2 + 6x3 + 3x4 + -1x5) = 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 '(-216 + 72x + -18x2 + 6x3 + 3x4 + -1x5)' equal to zero and attempt to solve: Simplifying -216 + 72x + -18x2 + 6x3 + 3x4 + -1x5 = 0 Solving -216 + 72x + -18x2 + 6x3 + 3x4 + -1x5 = 0 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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