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Simplifying (3a + 5b + -8c) + -1(2a + 5b + -12c) = 0 Remove parenthesis around (3a + 5b + -8c) 3a + 5b + -8c + -1(2a + 5b + -12c) = 0 3a + 5b + -8c + (2a * -1 + 5b * -1 + -12c * -1) = 0 3a + 5b + -8c + (-2a + -5b + 12c) = 0 Reorder the terms: 3a + -2a + 5b + -5b + -8c + 12c = 0 Combine like terms: 3a + -2a = 1a 1a + 5b + -5b + -8c + 12c = 0 Combine like terms: 5b + -5b = 0 1a + 0 + -8c + 12c = 0 1a + -8c + 12c = 0 Combine like terms: -8c + 12c = 4c 1a + 4c = 0 Solving 1a + 4c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-4c' to each side of the equation. 1a + 4c + -4c = 0 + -4c Combine like terms: 4c + -4c = 0 1a + 0 = 0 + -4c 1a = 0 + -4c Remove the zero: 1a = -4c Divide each side by '1'. a = -4c Simplifying a = -4c
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