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Simplifying -5a(3a2 + -6a) + -4(2a2 + -4a) = 0 Reorder the terms: -5a(-6a + 3a2) + -4(2a2 + -4a) = 0 (-6a * -5a + 3a2 * -5a) + -4(2a2 + -4a) = 0 (30a2 + -15a3) + -4(2a2 + -4a) = 0 Reorder the terms: 30a2 + -15a3 + -4(-4a + 2a2) = 0 30a2 + -15a3 + (-4a * -4 + 2a2 * -4) = 0 30a2 + -15a3 + (16a + -8a2) = 0 Reorder the terms: 16a + 30a2 + -8a2 + -15a3 = 0 Combine like terms: 30a2 + -8a2 = 22a2 16a + 22a2 + -15a3 = 0 Solving 16a + 22a2 + -15a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), 'a'. a(16 + 22a + -15a2) = 0 Factor a trinomial. a((2 + -1a)(8 + 15a)) = 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 '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Subproblem 3
Set the factor '(8 + 15a)' equal to zero and attempt to solve: Simplifying 8 + 15a = 0 Solving 8 + 15a = 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 + 15a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + 15a = 0 + -8 15a = 0 + -8 Combine like terms: 0 + -8 = -8 15a = -8 Divide each side by '15'. a = -0.5333333333 Simplifying a = -0.5333333333Solution
a = {0, 2, -0.5333333333}
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