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Simplifying 2a + 3b + -4c + -2(3a + 6b + -8c) + 3(4a + -6c) + 5a = 0 2a + 3b + -4c + (3a * -2 + 6b * -2 + -8c * -2) + 3(4a + -6c) + 5a = 0 2a + 3b + -4c + (-6a + -12b + 16c) + 3(4a + -6c) + 5a = 0 2a + 3b + -4c + -6a + -12b + 16c + (4a * 3 + -6c * 3) + 5a = 0 2a + 3b + -4c + -6a + -12b + 16c + (12a + -18c) + 5a = 0 Reorder the terms: 2a + -6a + 12a + 5a + 3b + -12b + -4c + 16c + -18c = 0 Combine like terms: 2a + -6a = -4a -4a + 12a + 5a + 3b + -12b + -4c + 16c + -18c = 0 Combine like terms: -4a + 12a = 8a 8a + 5a + 3b + -12b + -4c + 16c + -18c = 0 Combine like terms: 8a + 5a = 13a 13a + 3b + -12b + -4c + 16c + -18c = 0 Combine like terms: 3b + -12b = -9b 13a + -9b + -4c + 16c + -18c = 0 Combine like terms: -4c + 16c = 12c 13a + -9b + 12c + -18c = 0 Combine like terms: 12c + -18c = -6c 13a + -9b + -6c = 0 Solving 13a + -9b + -6c = 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 + -6c = 0 + 9b Combine like terms: -9b + 9b = 0 13a + 0 + -6c = 0 + 9b 13a + -6c = 0 + 9b Remove the zero: 13a + -6c = 9b Add '6c' to each side of the equation. 13a + -6c + 6c = 9b + 6c Combine like terms: -6c + 6c = 0 13a + 0 = 9b + 6c 13a = 9b + 6c Divide each side by '13'. a = 0.6923076923b + 0.4615384615c Simplifying a = 0.6923076923b + 0.4615384615c
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