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Simplifying 4x3 + 12ax2 + -16a2x = 0 Reorder the terms: 12ax2 + -16a2x + 4x3 = 0 Solving 12ax2 + -16a2x + 4x3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(3ax + -4a2 + x2) = 0 Factor a trinomial. 4x((-4a + -1x)(a + -1x)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing a to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-4a + -1x)' equal to zero and attempt to solve: Simplifying -4a + -1x = 0 Solving -4a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. -4a + -1x + x = 0 + x Combine like terms: -1x + x = 0 -4a + 0 = 0 + x -4a = 0 + x Remove the zero: -4a = x Divide each side by '-4'. a = -0.25x Simplifying a = -0.25xSubproblem 3
Set the factor '(a + -1x)' equal to zero and attempt to solve: Simplifying a + -1x = 0 Solving a + -1x = 0 Move all terms containing a to the left, all other terms to the right. Add 'x' to each side of the equation. a + -1x + x = 0 + x Combine like terms: -1x + x = 0 a + 0 = 0 + x a = 0 + x Remove the zero: a = x Simplifying a = xSolution
a = {-0.25x, x}
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