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Simplifying (a + 3)(3a + -1) = 0 Reorder the terms: (3 + a)(3a + -1) = 0 Reorder the terms: (3 + a)(-1 + 3a) = 0 Multiply (3 + a) * (-1 + 3a) (3(-1 + 3a) + a(-1 + 3a)) = 0 ((-1 * 3 + 3a * 3) + a(-1 + 3a)) = 0 ((-3 + 9a) + a(-1 + 3a)) = 0 (-3 + 9a + (-1 * a + 3a * a)) = 0 (-3 + 9a + (-1a + 3a2)) = 0 Combine like terms: 9a + -1a = 8a (-3 + 8a + 3a2) = 0 Solving -3 + 8a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (-3 + -1a)(1 + -3a) = 0Subproblem 1
Set the factor '(-3 + -1a)' equal to zero and attempt to solve: Simplifying -3 + -1a = 0 Solving -3 + -1a = 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 + -1a = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1a = 0 + 3 -1a = 0 + 3 Combine like terms: 0 + 3 = 3 -1a = 3 Divide each side by '-1'. a = -3 Simplifying a = -3Subproblem 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 = {-3, 0.3333333333}
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