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Simplifying 3a(a + -9)(a + 11) = 0 Reorder the terms: 3a(-9 + a)(a + 11) = 0 Reorder the terms: 3a(-9 + a)(11 + a) = 0 Multiply (-9 + a) * (11 + a) 3a(-9(11 + a) + a(11 + a)) = 0 3a((11 * -9 + a * -9) + a(11 + a)) = 0 3a((-99 + -9a) + a(11 + a)) = 0 3a(-99 + -9a + (11 * a + a * a)) = 0 3a(-99 + -9a + (11a + a2)) = 0 Combine like terms: -9a + 11a = 2a 3a(-99 + 2a + a2) = 0 (-99 * 3a + 2a * 3a + a2 * 3a) = 0 (-297a + 6a2 + 3a3) = 0 Solving -297a + 6a2 + 3a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '3a'. 3a(-99 + 2a + a2) = 0 Factor a trinomial. 3a((-11 + -1a)(9 + -1a)) = 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 '(-11 + -1a)' equal to zero and attempt to solve: Simplifying -11 + -1a = 0 Solving -11 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '11' to each side of the equation. -11 + 11 + -1a = 0 + 11 Combine like terms: -11 + 11 = 0 0 + -1a = 0 + 11 -1a = 0 + 11 Combine like terms: 0 + 11 = 11 -1a = 11 Divide each side by '-1'. a = -11 Simplifying a = -11Subproblem 3
Set the factor '(9 + -1a)' equal to zero and attempt to solve: Simplifying 9 + -1a = 0 Solving 9 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-9' to each side of the equation. 9 + -9 + -1a = 0 + -9 Combine like terms: 9 + -9 = 0 0 + -1a = 0 + -9 -1a = 0 + -9 Combine like terms: 0 + -9 = -9 -1a = -9 Divide each side by '-1'. a = 9 Simplifying a = 9Solution
a = {0, -11, 9}
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