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Simplifying 4a(2a + 5)(3a + -1) = 0 Reorder the terms: 4a(5 + 2a)(3a + -1) = 0 Reorder the terms: 4a(5 + 2a)(-1 + 3a) = 0 Multiply (5 + 2a) * (-1 + 3a) 4a(5(-1 + 3a) + 2a * (-1 + 3a)) = 0 4a((-1 * 5 + 3a * 5) + 2a * (-1 + 3a)) = 0 4a((-5 + 15a) + 2a * (-1 + 3a)) = 0 4a(-5 + 15a + (-1 * 2a + 3a * 2a)) = 0 4a(-5 + 15a + (-2a + 6a2)) = 0 Combine like terms: 15a + -2a = 13a 4a(-5 + 13a + 6a2) = 0 (-5 * 4a + 13a * 4a + 6a2 * 4a) = 0 (-20a + 52a2 + 24a3) = 0 Solving -20a + 52a2 + 24a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(-5 + 13a + 6a2) = 0 Factor a trinomial. 4a((-5 + -2a)(1 + -3a)) = 0 Ignore the factor 4.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 '(-5 + -2a)' equal to zero and attempt to solve: Simplifying -5 + -2a = 0 Solving -5 + -2a = 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 + -2a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -2a = 0 + 5 -2a = 0 + 5 Combine like terms: 0 + 5 = 5 -2a = 5 Divide each side by '-2'. a = -2.5 Simplifying a = -2.5Subproblem 3
Set the factor '(1 + -3a)' equal to zero and attempt to solve: Simplifying 1 + -3a = 0 Solving 1 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -3a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -3a = 0 + -1 -3a = 0 + -1 Combine like terms: 0 + -1 = -1 -3a = -1 Divide each side by '-3'. a = 0.3333333333 Simplifying a = 0.3333333333Solution
a = {0, -2.5, 0.3333333333}
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