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Simplifying (3a + 2)(3a + -1) = 0 Reorder the terms: (2 + 3a)(3a + -1) = 0 Reorder the terms: (2 + 3a)(-1 + 3a) = 0 Multiply (2 + 3a) * (-1 + 3a) (2(-1 + 3a) + 3a * (-1 + 3a)) = 0 ((-1 * 2 + 3a * 2) + 3a * (-1 + 3a)) = 0 ((-2 + 6a) + 3a * (-1 + 3a)) = 0 (-2 + 6a + (-1 * 3a + 3a * 3a)) = 0 (-2 + 6a + (-3a + 9a2)) = 0 Combine like terms: 6a + -3a = 3a (-2 + 3a + 9a2) = 0 Solving -2 + 3a + 9a2 = 0 Solving for variable 'a'. Factor a trinomial. (-2 + -3a)(1 + -3a) = 0Subproblem 1
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 = -0.6666666667Subproblem 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 = {-0.6666666667, 0.3333333333}
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