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Simplifying (3a + -7)(2 + -3a) + -1(2 + -3a)(4a + -15) = 0 Reorder the terms: (-7 + 3a)(2 + -3a) + -1(2 + -3a)(4a + -15) = 0 Multiply (-7 + 3a) * (2 + -3a) (-7(2 + -3a) + 3a * (2 + -3a)) + -1(2 + -3a)(4a + -15) = 0 ((2 * -7 + -3a * -7) + 3a * (2 + -3a)) + -1(2 + -3a)(4a + -15) = 0 ((-14 + 21a) + 3a * (2 + -3a)) + -1(2 + -3a)(4a + -15) = 0 (-14 + 21a + (2 * 3a + -3a * 3a)) + -1(2 + -3a)(4a + -15) = 0 (-14 + 21a + (6a + -9a2)) + -1(2 + -3a)(4a + -15) = 0 Combine like terms: 21a + 6a = 27a (-14 + 27a + -9a2) + -1(2 + -3a)(4a + -15) = 0 Reorder the terms: -14 + 27a + -9a2 + -1(2 + -3a)(-15 + 4a) = 0 Multiply (2 + -3a) * (-15 + 4a) -14 + 27a + -9a2 + -1(2(-15 + 4a) + -3a * (-15 + 4a)) = 0 -14 + 27a + -9a2 + -1((-15 * 2 + 4a * 2) + -3a * (-15 + 4a)) = 0 -14 + 27a + -9a2 + -1((-30 + 8a) + -3a * (-15 + 4a)) = 0 -14 + 27a + -9a2 + -1(-30 + 8a + (-15 * -3a + 4a * -3a)) = 0 -14 + 27a + -9a2 + -1(-30 + 8a + (45a + -12a2)) = 0 Combine like terms: 8a + 45a = 53a -14 + 27a + -9a2 + -1(-30 + 53a + -12a2) = 0 -14 + 27a + -9a2 + (-30 * -1 + 53a * -1 + -12a2 * -1) = 0 -14 + 27a + -9a2 + (30 + -53a + 12a2) = 0 Reorder the terms: -14 + 30 + 27a + -53a + -9a2 + 12a2 = 0 Combine like terms: -14 + 30 = 16 16 + 27a + -53a + -9a2 + 12a2 = 0 Combine like terms: 27a + -53a = -26a 16 + -26a + -9a2 + 12a2 = 0 Combine like terms: -9a2 + 12a2 = 3a2 16 + -26a + 3a2 = 0 Solving 16 + -26a + 3a2 = 0 Solving for variable 'a'. Factor a trinomial. (2 + -3a)(8 + -1a) = 0Subproblem 1
Set the factor '(2 + -3a)' equal to zero and attempt to solve: Simplifying 2 + -3a = 0 Solving 2 + -3a = 0 Move all terms containing a to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3a = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3a = 0 + -2 -3a = 0 + -2 Combine like terms: 0 + -2 = -2 -3a = -2 Divide each side by '-3'. a = 0.6666666667 Simplifying a = 0.6666666667Subproblem 2
Set the factor '(8 + -1a)' equal to zero and attempt to solve: Simplifying 8 + -1a = 0 Solving 8 + -1a = 0 Move all terms containing a to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + -1a = 0 + -8 Combine like terms: 8 + -8 = 0 0 + -1a = 0 + -8 -1a = 0 + -8 Combine like terms: 0 + -8 = -8 -1a = -8 Divide each side by '-1'. a = 8 Simplifying a = 8Solution
a = {0.6666666667, 8}
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