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Simplifying 5a(3a + -5)(5a + -1) = 0 Reorder the terms: 5a(-5 + 3a)(5a + -1) = 0 Reorder the terms: 5a(-5 + 3a)(-1 + 5a) = 0 Multiply (-5 + 3a) * (-1 + 5a) 5a(-5(-1 + 5a) + 3a * (-1 + 5a)) = 0 5a((-1 * -5 + 5a * -5) + 3a * (-1 + 5a)) = 0 5a((5 + -25a) + 3a * (-1 + 5a)) = 0 5a(5 + -25a + (-1 * 3a + 5a * 3a)) = 0 5a(5 + -25a + (-3a + 15a2)) = 0 Combine like terms: -25a + -3a = -28a 5a(5 + -28a + 15a2) = 0 (5 * 5a + -28a * 5a + 15a2 * 5a) = 0 (25a + -140a2 + 75a3) = 0 Solving 25a + -140a2 + 75a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(5 + -28a + 15a2) = 0 Factor a trinomial. 5a((1 + -5a)(5 + -3a)) = 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 '(1 + -5a)' equal to zero and attempt to solve: Simplifying 1 + -5a = 0 Solving 1 + -5a = 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 + -5a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -5a = 0 + -1 -5a = 0 + -1 Combine like terms: 0 + -1 = -1 -5a = -1 Divide each side by '-5'. a = 0.2 Simplifying a = 0.2Subproblem 3
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 = 1.666666667Solution
a = {0, 0.2, 1.666666667}
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