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Simplifying (4a + 6b + -3) + 3(a + -2b + 3) + -5(a + -1b + -3c) = 0 Reorder the terms: (-3 + 4a + 6b) + 3(a + -2b + 3) + -5(a + -1b + -3c) = 0 Remove parenthesis around (-3 + 4a + 6b) -3 + 4a + 6b + 3(a + -2b + 3) + -5(a + -1b + -3c) = 0 Reorder the terms: -3 + 4a + 6b + 3(3 + a + -2b) + -5(a + -1b + -3c) = 0 -3 + 4a + 6b + (3 * 3 + a * 3 + -2b * 3) + -5(a + -1b + -3c) = 0 -3 + 4a + 6b + (9 + 3a + -6b) + -5(a + -1b + -3c) = 0 -3 + 4a + 6b + 9 + 3a + -6b + (a * -5 + -1b * -5 + -3c * -5) = 0 -3 + 4a + 6b + 9 + 3a + -6b + (-5a + 5b + 15c) = 0 Reorder the terms: -3 + 9 + 4a + 3a + -5a + 6b + -6b + 5b + 15c = 0 Combine like terms: -3 + 9 = 6 6 + 4a + 3a + -5a + 6b + -6b + 5b + 15c = 0 Combine like terms: 4a + 3a = 7a 6 + 7a + -5a + 6b + -6b + 5b + 15c = 0 Combine like terms: 7a + -5a = 2a 6 + 2a + 6b + -6b + 5b + 15c = 0 Combine like terms: 6b + -6b = 0 6 + 2a + 0 + 5b + 15c = 0 6 + 2a + 5b + 15c = 0 Solving 6 + 2a + 5b + 15c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + 2a + 5b + -6 + 15c = 0 + -6 Reorder the terms: 6 + -6 + 2a + 5b + 15c = 0 + -6 Combine like terms: 6 + -6 = 0 0 + 2a + 5b + 15c = 0 + -6 2a + 5b + 15c = 0 + -6 Combine like terms: 0 + -6 = -6 2a + 5b + 15c = -6 Add '-5b' to each side of the equation. 2a + 5b + -5b + 15c = -6 + -5b Combine like terms: 5b + -5b = 0 2a + 0 + 15c = -6 + -5b 2a + 15c = -6 + -5b Add '-15c' to each side of the equation. 2a + 15c + -15c = -6 + -5b + -15c Combine like terms: 15c + -15c = 0 2a + 0 = -6 + -5b + -15c 2a = -6 + -5b + -15c Divide each side by '2'. a = -3 + -2.5b + -7.5c Simplifying a = -3 + -2.5b + -7.5c
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