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Simplifying a3 + -3a2 = 40a Reorder the terms: -3a2 + a3 = 40a Solving -3a2 + a3 = 40a Solving for variable 'a'. Reorder the terms: -40a + -3a2 + a3 = 40a + -40a Combine like terms: 40a + -40a = 0 -40a + -3a2 + a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(-40 + -3a + a2) = 0 Factor a trinomial. a((-5 + -1a)(8 + -1a)) = 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 '(-5 + -1a)' equal to zero and attempt to solve: Simplifying -5 + -1a = 0 Solving -5 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -1a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -1a = 0 + 5 -1a = 0 + 5 Combine like terms: 0 + 5 = 5 -1a = 5 Divide each side by '-1'. a = -5 Simplifying a = -5Subproblem 3
Set the factor '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8Solution
a = {0, -5, 8}
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