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Simplifying 5a(a + -4)(2a + -3) = 0 Reorder the terms: 5a(-4 + a)(2a + -3) = 0 Reorder the terms: 5a(-4 + a)(-3 + 2a) = 0 Multiply (-4 + a) * (-3 + 2a) 5a(-4(-3 + 2a) + a(-3 + 2a)) = 0 5a((-3 * -4 + 2a * -4) + a(-3 + 2a)) = 0 5a((12 + -8a) + a(-3 + 2a)) = 0 5a(12 + -8a + (-3 * a + 2a * a)) = 0 5a(12 + -8a + (-3a + 2a2)) = 0 Combine like terms: -8a + -3a = -11a 5a(12 + -11a + 2a2) = 0 (12 * 5a + -11a * 5a + 2a2 * 5a) = 0 (60a + -55a2 + 10a3) = 0 Solving 60a + -55a2 + 10a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(12 + -11a + 2a2) = 0 Factor a trinomial. 5a((3 + -2a)(4 + -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 '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Subproblem 3
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 = 4Solution
a = {0, 1.5, 4}
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