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Simplifying a(2a + 6)(a + -5) = 0 Reorder the terms: a(6 + 2a)(a + -5) = 0 Reorder the terms: a(6 + 2a)(-5 + a) = 0 Multiply (6 + 2a) * (-5 + a) a(6(-5 + a) + 2a * (-5 + a)) = 0 a((-5 * 6 + a * 6) + 2a * (-5 + a)) = 0 a((-30 + 6a) + 2a * (-5 + a)) = 0 a(-30 + 6a + (-5 * 2a + a * 2a)) = 0 a(-30 + 6a + (-10a + 2a2)) = 0 Combine like terms: 6a + -10a = -4a a(-30 + -4a + 2a2) = 0 (-30 * a + -4a * a + 2a2 * a) = 0 (-30a + -4a2 + 2a3) = 0 Solving -30a + -4a2 + 2a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2a'. 2a(-15 + -2a + a2) = 0 Factor a trinomial. 2a((-3 + -1a)(5 + -1a)) = 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 '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 3
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 = 5Solution
a = {0, -3, 5}
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