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Simplifying (13a + 9)(4a + -12) = 0 Reorder the terms: (9 + 13a)(4a + -12) = 0 Reorder the terms: (9 + 13a)(-12 + 4a) = 0 Multiply (9 + 13a) * (-12 + 4a) (9(-12 + 4a) + 13a * (-12 + 4a)) = 0 ((-12 * 9 + 4a * 9) + 13a * (-12 + 4a)) = 0 ((-108 + 36a) + 13a * (-12 + 4a)) = 0 (-108 + 36a + (-12 * 13a + 4a * 13a)) = 0 (-108 + 36a + (-156a + 52a2)) = 0 Combine like terms: 36a + -156a = -120a (-108 + -120a + 52a2) = 0 Solving -108 + -120a + 52a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '4'. 4(-27 + -30a + 13a2) = 0 Factor a trinomial. 4((-9 + -13a)(3 + -1a)) = 0 Ignore the factor 4.Subproblem 1
Set the factor '(-9 + -13a)' equal to zero and attempt to solve: Simplifying -9 + -13a = 0 Solving -9 + -13a = 0 Move all terms containing a to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 9 + -13a = 0 + 9 Combine like terms: -9 + 9 = 0 0 + -13a = 0 + 9 -13a = 0 + 9 Combine like terms: 0 + 9 = 9 -13a = 9 Divide each side by '-13'. a = -0.6923076923 Simplifying a = -0.6923076923Subproblem 2
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 = 3Solution
a = {-0.6923076923, 3}
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