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Simplifying 5a(4a2 + -5a + -6) + -3a(a + -2) = 0 Reorder the terms: 5a(-6 + -5a + 4a2) + -3a(a + -2) = 0 (-6 * 5a + -5a * 5a + 4a2 * 5a) + -3a(a + -2) = 0 (-30a + -25a2 + 20a3) + -3a(a + -2) = 0 Reorder the terms: -30a + -25a2 + 20a3 + -3a(-2 + a) = 0 -30a + -25a2 + 20a3 + (-2 * -3a + a * -3a) = 0 -30a + -25a2 + 20a3 + (6a + -3a2) = 0 Reorder the terms: -30a + 6a + -25a2 + -3a2 + 20a3 = 0 Combine like terms: -30a + 6a = -24a -24a + -25a2 + -3a2 + 20a3 = 0 Combine like terms: -25a2 + -3a2 = -28a2 -24a + -28a2 + 20a3 = 0 Solving -24a + -28a2 + 20a3 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4a'. 4a(-6 + -7a + 5a2) = 0 Factor a trinomial. 4a((-3 + -5a)(2 + -1a)) = 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 '(-3 + -5a)' equal to zero and attempt to solve: Simplifying -3 + -5a = 0 Solving -3 + -5a = 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 + -5a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -5a = 0 + 3 -5a = 0 + 3 Combine like terms: 0 + 3 = 3 -5a = 3 Divide each side by '-5'. a = -0.6 Simplifying a = -0.6Subproblem 3
Set the factor '(2 + -1a)' equal to zero and attempt to solve: Simplifying 2 + -1a = 0 Solving 2 + -1a = 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 + -1a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -1a = 0 + -2 -1a = 0 + -2 Combine like terms: 0 + -2 = -2 -1a = -2 Divide each side by '-1'. a = 2 Simplifying a = 2Solution
a = {0, -0.6, 2}
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