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Simplifying (5a + 8b) + -1[13 + -1(6a + 12b) + -14] = 0 Remove parenthesis around (5a + 8b) 5a + 8b + -1[13 + -1(6a + 12b) + -14] = 0 5a + 8b + -1[13 + (6a * -1 + 12b * -1) + -14] = 0 5a + 8b + -1[13 + (-6a + -12b) + -14] = 0 Reorder the terms: 5a + 8b + -1[13 + -14 + -6a + -12b] = 0 Combine like terms: 13 + -14 = -1 5a + 8b + -1[-1 + -6a + -12b] = 0 5a + 8b + [-1 * -1 + -6a * -1 + -12b * -1] = 0 5a + 8b + [1 + 6a + 12b] = 0 Reorder the terms: 1 + 5a + 6a + 8b + 12b = 0 Combine like terms: 5a + 6a = 11a 1 + 11a + 8b + 12b = 0 Combine like terms: 8b + 12b = 20b 1 + 11a + 20b = 0 Solving 1 + 11a + 20b = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + 11a + -1 + 20b = 0 + -1 Reorder the terms: 1 + -1 + 11a + 20b = 0 + -1 Combine like terms: 1 + -1 = 0 0 + 11a + 20b = 0 + -1 11a + 20b = 0 + -1 Combine like terms: 0 + -1 = -1 11a + 20b = -1 Add '-20b' to each side of the equation. 11a + 20b + -20b = -1 + -20b Combine like terms: 20b + -20b = 0 11a + 0 = -1 + -20b 11a = -1 + -20b Divide each side by '11'. a = -0.09090909091 + -1.818181818b Simplifying a = -0.09090909091 + -1.818181818b
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