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Simplifying (15a + -15)(-7a + 12) + -1(-9a + -8)(15a + -15) = 0 Reorder the terms: (-15 + 15a)(-7a + 12) + -1(-9a + -8)(15a + -15) = 0 Reorder the terms: (-15 + 15a)(12 + -7a) + -1(-9a + -8)(15a + -15) = 0 Multiply (-15 + 15a) * (12 + -7a) (-15(12 + -7a) + 15a * (12 + -7a)) + -1(-9a + -8)(15a + -15) = 0 ((12 * -15 + -7a * -15) + 15a * (12 + -7a)) + -1(-9a + -8)(15a + -15) = 0 ((-180 + 105a) + 15a * (12 + -7a)) + -1(-9a + -8)(15a + -15) = 0 (-180 + 105a + (12 * 15a + -7a * 15a)) + -1(-9a + -8)(15a + -15) = 0 (-180 + 105a + (180a + -105a2)) + -1(-9a + -8)(15a + -15) = 0 Combine like terms: 105a + 180a = 285a (-180 + 285a + -105a2) + -1(-9a + -8)(15a + -15) = 0 Reorder the terms: -180 + 285a + -105a2 + -1(-8 + -9a)(15a + -15) = 0 Reorder the terms: -180 + 285a + -105a2 + -1(-8 + -9a)(-15 + 15a) = 0 Multiply (-8 + -9a) * (-15 + 15a) -180 + 285a + -105a2 + -1(-8(-15 + 15a) + -9a * (-15 + 15a)) = 0 -180 + 285a + -105a2 + -1((-15 * -8 + 15a * -8) + -9a * (-15 + 15a)) = 0 -180 + 285a + -105a2 + -1((120 + -120a) + -9a * (-15 + 15a)) = 0 -180 + 285a + -105a2 + -1(120 + -120a + (-15 * -9a + 15a * -9a)) = 0 -180 + 285a + -105a2 + -1(120 + -120a + (135a + -135a2)) = 0 Combine like terms: -120a + 135a = 15a -180 + 285a + -105a2 + -1(120 + 15a + -135a2) = 0 -180 + 285a + -105a2 + (120 * -1 + 15a * -1 + -135a2 * -1) = 0 -180 + 285a + -105a2 + (-120 + -15a + 135a2) = 0 Reorder the terms: -180 + -120 + 285a + -15a + -105a2 + 135a2 = 0 Combine like terms: -180 + -120 = -300 -300 + 285a + -15a + -105a2 + 135a2 = 0 Combine like terms: 285a + -15a = 270a -300 + 270a + -105a2 + 135a2 = 0 Combine like terms: -105a2 + 135a2 = 30a2 -300 + 270a + 30a2 = 0 Solving -300 + 270a + 30a2 = 0 Solving for variable 'a'. Factor out the Greatest Common Factor (GCF), '30'. 30(-10 + 9a + a2) = 0 Factor a trinomial. 30((-10 + -1a)(1 + -1a)) = 0 Ignore the factor 30.Subproblem 1
Set the factor '(-10 + -1a)' equal to zero and attempt to solve: Simplifying -10 + -1a = 0 Solving -10 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '10' to each side of the equation. -10 + 10 + -1a = 0 + 10 Combine like terms: -10 + 10 = 0 0 + -1a = 0 + 10 -1a = 0 + 10 Combine like terms: 0 + 10 = 10 -1a = 10 Divide each side by '-1'. a = -10 Simplifying a = -10Subproblem 2
Set the factor '(1 + -1a)' equal to zero and attempt to solve: Simplifying 1 + -1a = 0 Solving 1 + -1a = 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 + -1a = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1a = 0 + -1 -1a = 0 + -1 Combine like terms: 0 + -1 = -1 -1a = -1 Divide each side by '-1'. a = 1 Simplifying a = 1Solution
a = {-10, 1}
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