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Simplifying 9a3 = 16a Solving 9a3 = 16a Solving for variable 'a'. Reorder the terms: -16a + 9a3 = 16a + -16a Combine like terms: 16a + -16a = 0 -16a + 9a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-16 + 9a2) = 0 Factor a difference between two squares. a((4 + 3a)(-4 + 3a)) = 0Subproblem 1
Set the factor 'a' equal to zero and attempt to solve: Simplifying a = 0 Solving a = 0 Move all terms containing a to the left, all other terms to the right. Simplifying a = 0Subproblem 2
Set the factor '(4 + 3a)' equal to zero and attempt to solve: Simplifying 4 + 3a = 0 Solving 4 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + 3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 3a = 0 + -4 3a = 0 + -4 Combine like terms: 0 + -4 = -4 3a = -4 Divide each side by '3'. a = -1.333333333 Simplifying a = -1.333333333Subproblem 3
Set the factor '(-4 + 3a)' equal to zero and attempt to solve: Simplifying -4 + 3a = 0 Solving -4 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + 3a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + 3a = 0 + 4 3a = 0 + 4 Combine like terms: 0 + 4 = 4 3a = 4 Divide each side by '3'. a = 1.333333333 Simplifying a = 1.333333333Solution
a = {0, -1.333333333, 1.333333333}
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