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Simplifying 0 = 2a(-1a + -7) + 3a(5a2 + a + 4) Reorder the terms: 0 = 2a(-7 + -1a) + 3a(5a2 + a + 4) 0 = (-7 * 2a + -1a * 2a) + 3a(5a2 + a + 4) 0 = (-14a + -2a2) + 3a(5a2 + a + 4) Reorder the terms: 0 = -14a + -2a2 + 3a(4 + a + 5a2) 0 = -14a + -2a2 + (4 * 3a + a * 3a + 5a2 * 3a) 0 = -14a + -2a2 + (12a + 3a2 + 15a3) Reorder the terms: 0 = -14a + 12a + -2a2 + 3a2 + 15a3 Combine like terms: -14a + 12a = -2a 0 = -2a + -2a2 + 3a2 + 15a3 Combine like terms: -2a2 + 3a2 = 1a2 0 = -2a + 1a2 + 15a3 Solving 0 = -2a + 1a2 + 15a3 Solving for variable 'a'. Remove the zero: 2a + -1a2 + -15a3 = -2a + 1a2 + 15a3 + 2a + -1a2 + -15a3 Reorder the terms: 2a + -1a2 + -15a3 = -2a + 2a + 1a2 + -1a2 + 15a3 + -15a3 Combine like terms: -2a + 2a = 0 2a + -1a2 + -15a3 = 0 + 1a2 + -1a2 + 15a3 + -15a3 2a + -1a2 + -15a3 = 1a2 + -1a2 + 15a3 + -15a3 Combine like terms: 1a2 + -1a2 = 0 2a + -1a2 + -15a3 = 0 + 15a3 + -15a3 2a + -1a2 + -15a3 = 15a3 + -15a3 Combine like terms: 15a3 + -15a3 = 0 2a + -1a2 + -15a3 = 0 Factor out the Greatest Common Factor (GCF), 'a'. a(2 + -1a + -15a2) = 0 Factor a trinomial. a((1 + -3a)(2 + 5a)) = 0Subproblem 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 + -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 = 0.3333333333Subproblem 3
Set the factor '(2 + 5a)' equal to zero and attempt to solve: Simplifying 2 + 5a = 0 Solving 2 + 5a = 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 + 5a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 5a = 0 + -2 5a = 0 + -2 Combine like terms: 0 + -2 = -2 5a = -2 Divide each side by '5'. a = -0.4 Simplifying a = -0.4Solution
a = {0, 0.3333333333, -0.4}
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