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Simplifying -4a(3a + -5)(2a + -1) = 0 Reorder the terms: -4a(-5 + 3a)(2a + -1) = 0 Reorder the terms: -4a(-5 + 3a)(-1 + 2a) = 0 Multiply (-5 + 3a) * (-1 + 2a) -4a(-5(-1 + 2a) + 3a * (-1 + 2a)) = 0 -4a((-1 * -5 + 2a * -5) + 3a * (-1 + 2a)) = 0 -4a((5 + -10a) + 3a * (-1 + 2a)) = 0 -4a(5 + -10a + (-1 * 3a + 2a * 3a)) = 0 -4a(5 + -10a + (-3a + 6a2)) = 0 Combine like terms: -10a + -3a = -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 + 3a)(1 + -2a)) = 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 + 3a)' equal to zero and attempt to solve: Simplifying -5 + 3a = 0 Solving -5 + 3a = 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 + 3a = 0 + 5 Combine like terms: -5 + 5 = 0 0 + 3a = 0 + 5 3a = 0 + 5 Combine like terms: 0 + 5 = 5 3a = 5 Divide each side by '3'. a = 1.666666667 Simplifying a = 1.666666667Subproblem 3
Set the factor '(1 + -2a)' equal to zero and attempt to solve: Simplifying 1 + -2a = 0 Solving 1 + -2a = 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 + -2a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -2a = 0 + -1 -2a = 0 + -1 Combine like terms: 0 + -1 = -1 -2a = -1 Divide each side by '-2'. a = 0.5 Simplifying a = 0.5Solution
a = {0, 1.666666667, 0.5}
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