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Simplifying 12X3 + 3X2 + -24X2 + -6X = 0 Reorder the terms: -6X + 3X2 + -24X2 + 12X3 = 0 Combine like terms: 3X2 + -24X2 = -21X2 -6X + -21X2 + 12X3 = 0 Solving -6X + -21X2 + 12X3 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), '3X'. 3X(-2 + -7X + 4X2) = 0 Factor a trinomial. 3X((-1 + -4X)(2 + -1X)) = 0 Ignore the factor 3.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 = 0Subproblem 2
Set the factor '(-1 + -4X)' equal to zero and attempt to solve: Simplifying -1 + -4X = 0 Solving -1 + -4X = 0 Move all terms containing X to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -4X = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -4X = 0 + 1 -4X = 0 + 1 Combine like terms: 0 + 1 = 1 -4X = 1 Divide each side by '-4'. X = -0.25 Simplifying X = -0.25Subproblem 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 = 2Solution
X = {0, -0.25, 2}
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