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Simplifying 3a(a + 12)(5a + -6) = 0 Reorder the terms: 3a(12 + a)(5a + -6) = 0 Reorder the terms: 3a(12 + a)(-6 + 5a) = 0 Multiply (12 + a) * (-6 + 5a) 3a(12(-6 + 5a) + a(-6 + 5a)) = 0 3a((-6 * 12 + 5a * 12) + a(-6 + 5a)) = 0 3a((-72 + 60a) + a(-6 + 5a)) = 0 3a(-72 + 60a + (-6 * a + 5a * a)) = 0 3a(-72 + 60a + (-6a + 5a2)) = 0 Combine like terms: 60a + -6a = 54a 3a(-72 + 54a + 5a2) = 0 (-72 * 3a + 54a * 3a + 5a2 * 3a) = 0 (-216a + 162a2 + 15a3) = 0 Solving -216a + 162a2 + 15a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(-72 + 54a + 5a2) = 0 Factor a trinomial. 3a((-12 + -1a)(6 + -5a)) = 0 Ignore the factor 3.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 '(-12 + -1a)' equal to zero and attempt to solve: Simplifying -12 + -1a = 0 Solving -12 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '12' to each side of the equation. -12 + 12 + -1a = 0 + 12 Combine like terms: -12 + 12 = 0 0 + -1a = 0 + 12 -1a = 0 + 12 Combine like terms: 0 + 12 = 12 -1a = 12 Divide each side by '-1'. a = -12 Simplifying a = -12Subproblem 3
Set the factor '(6 + -5a)' equal to zero and attempt to solve: Simplifying 6 + -5a = 0 Solving 6 + -5a = 0 Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -5a = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -5a = 0 + -6 -5a = 0 + -6 Combine like terms: 0 + -6 = -6 -5a = -6 Divide each side by '-5'. a = 1.2 Simplifying a = 1.2Solution
a = {0, -12, 1.2}
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