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Simplifying 40a2 + 20a + -30 = (-1)(15a3 + 30) Reorder the terms: -30 + 20a + 40a2 = (-1)(15a3 + 30) Reorder the terms: -30 + 20a + 40a2 = -1(30 + 15a3) -30 + 20a + 40a2 = (30 * -1 + 15a3 * -1) -30 + 20a + 40a2 = (-30 + -15a3) Add '30' to each side of the equation. -30 + 20a + 30 + 40a2 = -30 + 30 + -15a3 Reorder the terms: -30 + 30 + 20a + 40a2 = -30 + 30 + -15a3 Combine like terms: -30 + 30 = 0 0 + 20a + 40a2 = -30 + 30 + -15a3 20a + 40a2 = -30 + 30 + -15a3 Combine like terms: -30 + 30 = 0 20a + 40a2 = 0 + -15a3 20a + 40a2 = -15a3 Solving 20a + 40a2 = -15a3 Solving for variable 'a'. Combine like terms: -15a3 + 15a3 = 0 20a + 40a2 + 15a3 = 0 Factor out the Greatest Common Factor (GCF), '5a'. 5a(4 + 8a + 3a2) = 0 Factor a trinomial. 5a((2 + a)(2 + 3a)) = 0 Ignore the factor 5.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 '(2 + a)' equal to zero and attempt to solve: Simplifying 2 + a = 0 Solving 2 + a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + a = 0 + -2 a = 0 + -2 Combine like terms: 0 + -2 = -2 a = -2 Simplifying a = -2Subproblem 3
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {0, -2, -0.6666666667}
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