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Simplifying 5(6a + -3b + 7c) + 3(5a + -3b + 6) = 0 (6a * 5 + -3b * 5 + 7c * 5) + 3(5a + -3b + 6) = 0 (30a + -15b + 35c) + 3(5a + -3b + 6) = 0 Reorder the terms: 30a + -15b + 35c + 3(6 + 5a + -3b) = 0 30a + -15b + 35c + (6 * 3 + 5a * 3 + -3b * 3) = 0 30a + -15b + 35c + (18 + 15a + -9b) = 0 Reorder the terms: 18 + 30a + 15a + -15b + -9b + 35c = 0 Combine like terms: 30a + 15a = 45a 18 + 45a + -15b + -9b + 35c = 0 Combine like terms: -15b + -9b = -24b 18 + 45a + -24b + 35c = 0 Solving 18 + 45a + -24b + 35c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-18' to each side of the equation. 18 + 45a + -24b + -18 + 35c = 0 + -18 Reorder the terms: 18 + -18 + 45a + -24b + 35c = 0 + -18 Combine like terms: 18 + -18 = 0 0 + 45a + -24b + 35c = 0 + -18 45a + -24b + 35c = 0 + -18 Combine like terms: 0 + -18 = -18 45a + -24b + 35c = -18 Add '24b' to each side of the equation. 45a + -24b + 24b + 35c = -18 + 24b Combine like terms: -24b + 24b = 0 45a + 0 + 35c = -18 + 24b 45a + 35c = -18 + 24b Add '-35c' to each side of the equation. 45a + 35c + -35c = -18 + 24b + -35c Combine like terms: 35c + -35c = 0 45a + 0 = -18 + 24b + -35c 45a = -18 + 24b + -35c Divide each side by '45'. a = -0.4 + 0.5333333333b + -0.7777777778c Simplifying a = -0.4 + 0.5333333333b + -0.7777777778c
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