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Simplifying (a + 2b + 3c) + -1(4a + 6b + -5c) = 0 Remove parenthesis around (a + 2b + 3c) a + 2b + 3c + -1(4a + 6b + -5c) = 0 a + 2b + 3c + (4a * -1 + 6b * -1 + -5c * -1) = 0 a + 2b + 3c + (-4a + -6b + 5c) = 0 Reorder the terms: a + -4a + 2b + -6b + 3c + 5c = 0 Combine like terms: a + -4a = -3a -3a + 2b + -6b + 3c + 5c = 0 Combine like terms: 2b + -6b = -4b -3a + -4b + 3c + 5c = 0 Combine like terms: 3c + 5c = 8c -3a + -4b + 8c = 0 Solving -3a + -4b + 8c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '4b' to each side of the equation. -3a + -4b + 4b + 8c = 0 + 4b Combine like terms: -4b + 4b = 0 -3a + 0 + 8c = 0 + 4b -3a + 8c = 0 + 4b Remove the zero: -3a + 8c = 4b Add '-8c' to each side of the equation. -3a + 8c + -8c = 4b + -8c Combine like terms: 8c + -8c = 0 -3a + 0 = 4b + -8c -3a = 4b + -8c Divide each side by '-3'. a = -1.333333333b + 2.666666667c Simplifying a = -1.333333333b + 2.666666667c
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