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Simplifying (-13a + 4)(6a + -12) + -1(-4a + -2)(-13a + 4) = 0 Reorder the terms: (4 + -13a)(6a + -12) + -1(-4a + -2)(-13a + 4) = 0 Reorder the terms: (4 + -13a)(-12 + 6a) + -1(-4a + -2)(-13a + 4) = 0 Multiply (4 + -13a) * (-12 + 6a) (4(-12 + 6a) + -13a * (-12 + 6a)) + -1(-4a + -2)(-13a + 4) = 0 ((-12 * 4 + 6a * 4) + -13a * (-12 + 6a)) + -1(-4a + -2)(-13a + 4) = 0 ((-48 + 24a) + -13a * (-12 + 6a)) + -1(-4a + -2)(-13a + 4) = 0 (-48 + 24a + (-12 * -13a + 6a * -13a)) + -1(-4a + -2)(-13a + 4) = 0 (-48 + 24a + (156a + -78a2)) + -1(-4a + -2)(-13a + 4) = 0 Combine like terms: 24a + 156a = 180a (-48 + 180a + -78a2) + -1(-4a + -2)(-13a + 4) = 0 Reorder the terms: -48 + 180a + -78a2 + -1(-2 + -4a)(-13a + 4) = 0 Reorder the terms: -48 + 180a + -78a2 + -1(-2 + -4a)(4 + -13a) = 0 Multiply (-2 + -4a) * (4 + -13a) -48 + 180a + -78a2 + -1(-2(4 + -13a) + -4a * (4 + -13a)) = 0 -48 + 180a + -78a2 + -1((4 * -2 + -13a * -2) + -4a * (4 + -13a)) = 0 -48 + 180a + -78a2 + -1((-8 + 26a) + -4a * (4 + -13a)) = 0 -48 + 180a + -78a2 + -1(-8 + 26a + (4 * -4a + -13a * -4a)) = 0 -48 + 180a + -78a2 + -1(-8 + 26a + (-16a + 52a2)) = 0 Combine like terms: 26a + -16a = 10a -48 + 180a + -78a2 + -1(-8 + 10a + 52a2) = 0 -48 + 180a + -78a2 + (-8 * -1 + 10a * -1 + 52a2 * -1) = 0 -48 + 180a + -78a2 + (8 + -10a + -52a2) = 0 Reorder the terms: -48 + 8 + 180a + -10a + -78a2 + -52a2 = 0 Combine like terms: -48 + 8 = -40 -40 + 180a + -10a + -78a2 + -52a2 = 0 Combine like terms: 180a + -10a = 170a -40 + 170a + -78a2 + -52a2 = 0 Combine like terms: -78a2 + -52a2 = -130a2 -40 + 170a + -130a2 = 0 Solving -40 + 170a + -130a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '10'. 10(-4 + 17a + -13a2) = 0 Factor a trinomial. 10((-1 + a)(4 + -13a)) = 0 Ignore the factor 10.Subproblem 1
Set the factor '(-1 + a)' equal to zero and attempt to solve: Simplifying -1 + a = 0 Solving -1 + a = 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 + a = 0 + 1 Combine like terms: -1 + 1 = 0 0 + a = 0 + 1 a = 0 + 1 Combine like terms: 0 + 1 = 1 a = 1 Simplifying a = 1Subproblem 2
Set the factor '(4 + -13a)' equal to zero and attempt to solve: Simplifying 4 + -13a = 0 Solving 4 + -13a = 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 + -13a = 0 + -4 Combine like terms: 4 + -4 = 0 0 + -13a = 0 + -4 -13a = 0 + -4 Combine like terms: 0 + -4 = -4 -13a = -4 Divide each side by '-13'. a = 0.3076923077 Simplifying a = 0.3076923077Solution
a = {1, 0.3076923077}
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