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Simplifying (6a + -3b + -5c) + -1(a + -16b + 13c) = 0 Remove parenthesis around (6a + -3b + -5c) 6a + -3b + -5c + -1(a + -16b + 13c) = 0 6a + -3b + -5c + (a * -1 + -16b * -1 + 13c * -1) = 0 6a + -3b + -5c + (-1a + 16b + -13c) = 0 Reorder the terms: 6a + -1a + -3b + 16b + -5c + -13c = 0 Combine like terms: 6a + -1a = 5a 5a + -3b + 16b + -5c + -13c = 0 Combine like terms: -3b + 16b = 13b 5a + 13b + -5c + -13c = 0 Combine like terms: -5c + -13c = -18c 5a + 13b + -18c = 0 Solving 5a + 13b + -18c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-13b' to each side of the equation. 5a + 13b + -13b + -18c = 0 + -13b Combine like terms: 13b + -13b = 0 5a + 0 + -18c = 0 + -13b 5a + -18c = 0 + -13b Remove the zero: 5a + -18c = -13b Add '18c' to each side of the equation. 5a + -18c + 18c = -13b + 18c Combine like terms: -18c + 18c = 0 5a + 0 = -13b + 18c 5a = -13b + 18c Divide each side by '5'. a = -2.6b + 3.6c Simplifying a = -2.6b + 3.6c
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