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Simplifying (6a + 2)(3a + -2) = 0 Reorder the terms: (2 + 6a)(3a + -2) = 0 Reorder the terms: (2 + 6a)(-2 + 3a) = 0 Multiply (2 + 6a) * (-2 + 3a) (2(-2 + 3a) + 6a * (-2 + 3a)) = 0 ((-2 * 2 + 3a * 2) + 6a * (-2 + 3a)) = 0 ((-4 + 6a) + 6a * (-2 + 3a)) = 0 (-4 + 6a + (-2 * 6a + 3a * 6a)) = 0 (-4 + 6a + (-12a + 18a2)) = 0 Combine like terms: 6a + -12a = -6a (-4 + -6a + 18a2) = 0 Solving -4 + -6a + 18a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-2 + -3a + 9a2) = 0 Factor a trinomial. 2((-1 + -3a)(2 + -3a)) = 0 Ignore the factor 2.Subproblem 1
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 2
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 = 0.6666666667Solution
a = {-0.3333333333, 0.6666666667}
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