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Simplifying 5a(a + -5)(a + 6) = 0 Reorder the terms: 5a(-5 + a)(a + 6) = 0 Reorder the terms: 5a(-5 + a)(6 + a) = 0 Multiply (-5 + a) * (6 + a) 5a(-5(6 + a) + a(6 + a)) = 0 5a((6 * -5 + a * -5) + a(6 + a)) = 0 5a((-30 + -5a) + a(6 + a)) = 0 5a(-30 + -5a + (6 * a + a * a)) = 0 5a(-30 + -5a + (6a + a2)) = 0 Combine like terms: -5a + 6a = 1a 5a(-30 + 1a + a2) = 0 (-30 * 5a + 1a * 5a + a2 * 5a) = 0 (-150a + 5a2 + 5a3) = 0 Solving -150a + 5a2 + 5a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(-30 + a + a2) = 0 Factor a trinomial. 5a((-6 + -1a)(5 + -1a)) = 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 '(-6 + -1a)' equal to zero and attempt to solve: Simplifying -6 + -1a = 0 Solving -6 + -1a = 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 + -1a = 0 + 6 Combine like terms: -6 + 6 = 0 0 + -1a = 0 + 6 -1a = 0 + 6 Combine like terms: 0 + 6 = 6 -1a = 6 Divide each side by '-1'. a = -6 Simplifying a = -6Subproblem 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, -6, 5}
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