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Simplifying 48a2x + -20ax + -12x = 0 Reorder the terms: -20ax + 48a2x + -12x = 0 Solving -20ax + 48a2x + -12x = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-5a + 12a2 + -3) = 0 Factor a trinomial. 4x((4a + -3)(3a + 1)) = 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 + -3)' equal to zero and attempt to solve: Simplifying 4a + -3 = 0 Reorder the terms: -3 + 4a = 0 Solving -3 + 4a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 4a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 4a = 0 + 3 4a = 0 + 3 Combine like terms: 0 + 3 = 3 4a = 3 Divide each side by '4'. a = 0.75 Simplifying a = 0.75Subproblem 3
Set the factor '(3a + 1)' equal to zero and attempt to solve: Simplifying 3a + 1 = 0 Reorder the terms: 1 + 3a = 0 Solving 1 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + 3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 3a = 0 + -1 3a = 0 + -1 Combine like terms: 0 + -1 = -1 3a = -1 Divide each side by '3'. a = -0.3333333333 Simplifying a = -0.3333333333Solution
a = {0.75, -0.3333333333}
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