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Simplifying 5a(a + -3)(a + 4) = 0 Reorder the terms: 5a(-3 + a)(a + 4) = 0 Reorder the terms: 5a(-3 + a)(4 + a) = 0 Multiply (-3 + a) * (4 + a) 5a(-3(4 + a) + a(4 + a)) = 0 5a((4 * -3 + a * -3) + a(4 + a)) = 0 5a((-12 + -3a) + a(4 + a)) = 0 5a(-12 + -3a + (4 * a + a * a)) = 0 5a(-12 + -3a + (4a + a2)) = 0 Combine like terms: -3a + 4a = 1a 5a(-12 + 1a + a2) = 0 (-12 * 5a + 1a * 5a + a2 * 5a) = 0 (-60a + 5a2 + 5a3) = 0 Solving -60a + 5a2 + 5a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(-12 + a + a2) = 0 Factor a trinomial. 5a((-4 + -1a)(3 + -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 '(-4 + -1a)' equal to zero and attempt to solve: Simplifying -4 + -1a = 0 Solving -4 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1a = 0 + 4 -1a = 0 + 4 Combine like terms: 0 + 4 = 4 -1a = 4 Divide each side by '-1'. a = -4 Simplifying a = -4Subproblem 3
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 = 3Solution
a = {0, -4, 3}
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