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Simplifying (5a + 9b + -10c) + 3(-6a + 7c) = 0 Remove parenthesis around (5a + 9b + -10c) 5a + 9b + -10c + 3(-6a + 7c) = 0 5a + 9b + -10c + (-6a * 3 + 7c * 3) = 0 5a + 9b + -10c + (-18a + 21c) = 0 Reorder the terms: 5a + -18a + 9b + -10c + 21c = 0 Combine like terms: 5a + -18a = -13a -13a + 9b + -10c + 21c = 0 Combine like terms: -10c + 21c = 11c -13a + 9b + 11c = 0 Solving -13a + 9b + 11c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-9b' to each side of the equation. -13a + 9b + -9b + 11c = 0 + -9b Combine like terms: 9b + -9b = 0 -13a + 0 + 11c = 0 + -9b -13a + 11c = 0 + -9b Remove the zero: -13a + 11c = -9b Add '-11c' to each side of the equation. -13a + 11c + -11c = -9b + -11c Combine like terms: 11c + -11c = 0 -13a + 0 = -9b + -11c -13a = -9b + -11c Divide each side by '-13'. a = 0.6923076923b + 0.8461538462c Simplifying a = 0.6923076923b + 0.8461538462c
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