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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((-4 + a)(3 + -2a)) = 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 + a)' equal to zero and attempt to solve: Simplifying -4 + a = 0 Solving -4 + a = 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 + a = 0 + 4 Combine like terms: -4 + 4 = 0 0 + a = 0 + 4 a = 0 + 4 Combine like terms: 0 + 4 = 4 a = 4 Simplifying a = 4Subproblem 3
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 = 1.5Solution
a = {0, 4, 1.5}
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