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Simplifying 32a3z + 24a2z + -36az = 0 Reorder the terms: -36az + 24a2z + 32a3z = 0 Solving -36az + 24a2z + 32a3z = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4az'. 4az(-9 + 6a + 8a2) = 0 Factor a trinomial. 4az((-3 + -2a)(3 + -4a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor 'az' equal to zero and attempt to solve: Simplifying az = 0 Solving az = 0 Move all terms containing a to the left, all other terms to the right. Simplifying az = 0 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 '(-3 + -2a)' equal to zero and attempt to solve: Simplifying -3 + -2a = 0 Solving -3 + -2a = 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 + -2a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -2a = 0 + 3 -2a = 0 + 3 Combine like terms: 0 + 3 = 3 -2a = 3 Divide each side by '-2'. a = -1.5 Simplifying a = -1.5Subproblem 3
Set the factor '(3 + -4a)' equal to zero and attempt to solve: Simplifying 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 = 0.75Solution
a = {-1.5, 0.75}
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