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Simplifying (3a + -4)(4a + -6) = 0 Reorder the terms: (-4 + 3a)(4a + -6) = 0 Reorder the terms: (-4 + 3a)(-6 + 4a) = 0 Multiply (-4 + 3a) * (-6 + 4a) (-4(-6 + 4a) + 3a * (-6 + 4a)) = 0 ((-6 * -4 + 4a * -4) + 3a * (-6 + 4a)) = 0 ((24 + -16a) + 3a * (-6 + 4a)) = 0 (24 + -16a + (-6 * 3a + 4a * 3a)) = 0 (24 + -16a + (-18a + 12a2)) = 0 Combine like terms: -16a + -18a = -34a (24 + -34a + 12a2) = 0 Solving 24 + -34a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(12 + -17a + 6a2) = 0 Factor a trinomial. 2((4 + -3a)(3 + -2a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(4 + -3a)' equal to zero and attempt to solve: Simplifying 4 + -3a = 0 Solving 4 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + -4 + -3a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -3a = 0 + -4 -3a = 0 + -4 Combine like terms: 0 + -4 = -4 -3a = -4 Divide each side by '-3'. a = 1.333333333 Simplifying a = 1.333333333Subproblem 2
Set the factor '(3 + -2a)' equal to zero and attempt to solve: Simplifying 3 + -2a = 0 Solving 3 + -2a = 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 + -2a = 0 + -3 Combine like terms: 3 + -3 = 0 0 + -2a = 0 + -3 -2a = 0 + -3 Combine like terms: 0 + -3 = -3 -2a = -3 Divide each side by '-2'. a = 1.5 Simplifying a = 1.5Solution
a = {1.333333333, 1.5}
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