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Simplifying 0 = 2a3 + 18a2 + 40a Reorder the terms: 0 = 40a + 18a2 + 2a3 Solving 0 = 40a + 18a2 + 2a3 Solving for variable 'a'. Remove the zero: -40a + -18a2 + -2a3 = 40a + 18a2 + 2a3 + -40a + -18a2 + -2a3 Reorder the terms: -40a + -18a2 + -2a3 = 40a + -40a + 18a2 + -18a2 + 2a3 + -2a3 Combine like terms: 40a + -40a = 0 -40a + -18a2 + -2a3 = 0 + 18a2 + -18a2 + 2a3 + -2a3 -40a + -18a2 + -2a3 = 18a2 + -18a2 + 2a3 + -2a3 Combine like terms: 18a2 + -18a2 = 0 -40a + -18a2 + -2a3 = 0 + 2a3 + -2a3 -40a + -18a2 + -2a3 = 2a3 + -2a3 Combine like terms: 2a3 + -2a3 = 0 -40a + -18a2 + -2a3 = 0 Factor out the Greatest Common Factor (GCF), '-2a'. -2a(20 + 9a + a2) = 0 Factor a trinomial. -2a((5 + a)(4 + a)) = 0 Ignore the factor -2.Subproblem 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 + a)' equal to zero and attempt to solve: Simplifying 5 + a = 0 Solving 5 + a = 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 + a = 0 + -5 Combine like terms: 5 + -5 = 0 0 + a = 0 + -5 a = 0 + -5 Combine like terms: 0 + -5 = -5 a = -5 Simplifying a = -5Subproblem 3
Set the factor '(4 + a)' equal to zero and attempt to solve: Simplifying 4 + a = 0 Solving 4 + a = 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 + a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + a = 0 + -4 a = 0 + -4 Combine like terms: 0 + -4 = -4 a = -4 Simplifying a = -4Solution
a = {0, -5, -4}
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