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Simplifying (3a + -7)(4b + -5) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 Reorder the terms: (-7 + 3a)(4b + -5) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 Reorder the terms: (-7 + 3a)(-5 + 4b) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 Multiply (-7 + 3a) * (-5 + 4b) (-7(-5 + 4b) + 3a * (-5 + 4b)) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 ((-5 * -7 + 4b * -7) + 3a * (-5 + 4b)) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 ((35 + -28b) + 3a * (-5 + 4b)) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 (35 + -28b + (-5 * 3a + 4b * 3a)) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 (35 + -28b + (-15a + 12ab)) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 Reorder the terms: (35 + -15a + 12ab + -28b) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 (35 + -15a + 12ab + -28b) + -1(6a + -1)(2b + 9) + -1(a + -26b) = 0 Reorder the terms: 35 + -15a + 12ab + -28b + -1(-1 + 6a)(2b + 9) + -1(a + -26b) = 0 Reorder the terms: 35 + -15a + 12ab + -28b + -1(-1 + 6a)(9 + 2b) + -1(a + -26b) = 0 Multiply (-1 + 6a) * (9 + 2b) 35 + -15a + 12ab + -28b + -1(-1(9 + 2b) + 6a * (9 + 2b)) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + -1((9 * -1 + 2b * -1) + 6a * (9 + 2b)) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + -1((-9 + -2b) + 6a * (9 + 2b)) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + -1(-9 + -2b + (9 * 6a + 2b * 6a)) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + -1(-9 + -2b + (54a + 12ab)) + -1(a + -26b) = 0 Reorder the terms: 35 + -15a + 12ab + -28b + -1(-9 + 54a + 12ab + -2b) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + -1(-9 + 54a + 12ab + -2b) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + (-9 * -1 + 54a * -1 + 12ab * -1 + -2b * -1) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + (9 + -54a + -12ab + 2b) + -1(a + -26b) = 0 35 + -15a + 12ab + -28b + 9 + -54a + -12ab + 2b + (a * -1 + -26b * -1) = 0 35 + -15a + 12ab + -28b + 9 + -54a + -12ab + 2b + (-1a + 26b) = 0 Reorder the terms: 35 + 9 + -15a + -54a + -1a + 12ab + -12ab + -28b + 2b + 26b = 0 Combine like terms: 35 + 9 = 44 44 + -15a + -54a + -1a + 12ab + -12ab + -28b + 2b + 26b = 0 Combine like terms: -15a + -54a = -69a 44 + -69a + -1a + 12ab + -12ab + -28b + 2b + 26b = 0 Combine like terms: -69a + -1a = -70a 44 + -70a + 12ab + -12ab + -28b + 2b + 26b = 0 Combine like terms: 12ab + -12ab = 0 44 + -70a + 0 + -28b + 2b + 26b = 0 44 + -70a + -28b + 2b + 26b = 0 Combine like terms: -28b + 2b = -26b 44 + -70a + -26b + 26b = 0 Combine like terms: -26b + 26b = 0 44 + -70a + 0 = 0 44 + -70a = 0 Solving 44 + -70a = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-44' to each side of the equation. 44 + -44 + -70a = 0 + -44 Combine like terms: 44 + -44 = 0 0 + -70a = 0 + -44 -70a = 0 + -44 Combine like terms: 0 + -44 = -44 -70a = -44 Divide each side by '-70'. a = 0.6285714286 Simplifying a = 0.6285714286
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