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Simplifying 12x5 + -21x3 = 108x Reorder the terms: -21x3 + 12x5 = 108x Solving -21x3 + 12x5 = 108x Solving for variable 'x'. Reorder the terms: -108x + -21x3 + 12x5 = 108x + -108x Combine like terms: 108x + -108x = 0 -108x + -21x3 + 12x5 = 0 Factor out the Greatest Common Factor (GCF), '3x'. 3x(-36 + -7x2 + 4x4) = 0 Factor a trinomial. 3x((-9 + -4x2)(4 + -1x2)) = 0 Factor a difference between two squares. 3x((-9 + -4x2)((2 + x)(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 '(-9 + -4x2)' equal to zero and attempt to solve: Simplifying -9 + -4x2 = 0 Solving -9 + -4x2 = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -4x2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -4x2 = 0 + 9 -4x2 = 0 + 9 Combine like terms: 0 + 9 = 9 -4x2 = 9 Divide each side by '-4'. x2 = -2.25 Simplifying x2 = -2.25 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 Simplifying x = -2Subproblem 4
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, -2, 2}
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