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Simplifying (3a + -4)(4a + 2) = 0 Reorder the terms: (-4 + 3a)(4a + 2) = 0 Reorder the terms: (-4 + 3a)(2 + 4a) = 0 Multiply (-4 + 3a) * (2 + 4a) (-4(2 + 4a) + 3a * (2 + 4a)) = 0 ((2 * -4 + 4a * -4) + 3a * (2 + 4a)) = 0 ((-8 + -16a) + 3a * (2 + 4a)) = 0 (-8 + -16a + (2 * 3a + 4a * 3a)) = 0 (-8 + -16a + (6a + 12a2)) = 0 Combine like terms: -16a + 6a = -10a (-8 + -10a + 12a2) = 0 Solving -8 + -10a + 12a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '2'. 2(-4 + -5a + 6a2) = 0 Factor a trinomial. 2((-1 + -2a)(4 + -3a)) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-1 + -2a)' equal to zero and attempt to solve: Simplifying -1 + -2a = 0 Solving -1 + -2a = 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 + -2a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -2a = 0 + 1 -2a = 0 + 1 Combine like terms: 0 + 1 = 1 -2a = 1 Divide each side by '-2'. a = -0.5 Simplifying a = -0.5Subproblem 2
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 = 1.333333333Solution
a = {-0.5, 1.333333333}
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