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Simplifying 3a + -3 = 15a2 + 2a + -5 Reorder the terms: -3 + 3a = 15a2 + 2a + -5 Reorder the terms: -3 + 3a = -5 + 2a + 15a2 Solving -3 + 3a = -5 + 2a + 15a2 Solving for variable 'a'. Reorder the terms: -3 + 5 + 3a + -2a + -15a2 = -5 + 2a + 15a2 + 5 + -2a + -15a2 Combine like terms: -3 + 5 = 2 2 + 3a + -2a + -15a2 = -5 + 2a + 15a2 + 5 + -2a + -15a2 Combine like terms: 3a + -2a = 1a 2 + 1a + -15a2 = -5 + 2a + 15a2 + 5 + -2a + -15a2 Reorder the terms: 2 + 1a + -15a2 = -5 + 5 + 2a + -2a + 15a2 + -15a2 Combine like terms: -5 + 5 = 0 2 + 1a + -15a2 = 0 + 2a + -2a + 15a2 + -15a2 2 + 1a + -15a2 = 2a + -2a + 15a2 + -15a2 Combine like terms: 2a + -2a = 0 2 + 1a + -15a2 = 0 + 15a2 + -15a2 2 + 1a + -15a2 = 15a2 + -15a2 Combine like terms: 15a2 + -15a2 = 0 2 + 1a + -15a2 = 0 Factor a trinomial. (2 + -5a)(1 + 3a) = 0Subproblem 1
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 = 0.4Subproblem 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 = -0.3333333333Solution
a = {0.4, -0.3333333333}
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