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Simplifying -5a(a + -1)(3a + 2) = 0 Reorder the terms: -5a(-1 + a)(3a + 2) = 0 Reorder the terms: -5a(-1 + a)(2 + 3a) = 0 Multiply (-1 + a) * (2 + 3a) -5a(-1(2 + 3a) + a(2 + 3a)) = 0 -5a((2 * -1 + 3a * -1) + a(2 + 3a)) = 0 -5a((-2 + -3a) + a(2 + 3a)) = 0 -5a(-2 + -3a + (2 * a + 3a * a)) = 0 -5a(-2 + -3a + (2a + 3a2)) = 0 Combine like terms: -3a + 2a = -1a -5a(-2 + -1a + 3a2) = 0 (-2 * -5a + -1a * -5a + 3a2 * -5a) = 0 (10a + 5a2 + -15a3) = 0 Solving 10a + 5a2 + -15a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '5a'. 5a(2 + a + -3a2) = 0 Factor a trinomial. 5a((1 + -1a)(2 + 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 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Subproblem 3
Set the factor '(2 + 3a)' equal to zero and attempt to solve: Simplifying 2 + 3a = 0 Solving 2 + 3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + 3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3a = 0 + -2 3a = 0 + -2 Combine like terms: 0 + -2 = -2 3a = -2 Divide each side by '3'. a = -0.6666666667 Simplifying a = -0.6666666667Solution
a = {0, 1, -0.6666666667}
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