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Simplifying -1(3a + 5b) + (-2a + -1b) + -1(6b + 3c) + -6c = 0 (3a * -1 + 5b * -1) + (-2a + -1b) + -1(6b + 3c) + -6c = 0 (-3a + -5b) + (-2a + -1b) + -1(6b + 3c) + -6c = 0 Remove parenthesis around (-2a + -1b) -3a + -5b + -2a + -1b + -1(6b + 3c) + -6c = 0 -3a + -5b + -2a + -1b + (6b * -1 + 3c * -1) + -6c = 0 -3a + -5b + -2a + -1b + (-6b + -3c) + -6c = 0 Reorder the terms: -3a + -2a + -5b + -1b + -6b + -3c + -6c = 0 Combine like terms: -3a + -2a = -5a -5a + -5b + -1b + -6b + -3c + -6c = 0 Combine like terms: -5b + -1b = -6b -5a + -6b + -6b + -3c + -6c = 0 Combine like terms: -6b + -6b = -12b -5a + -12b + -3c + -6c = 0 Combine like terms: -3c + -6c = -9c -5a + -12b + -9c = 0 Solving -5a + -12b + -9c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '12b' to each side of the equation. -5a + -12b + 12b + -9c = 0 + 12b Combine like terms: -12b + 12b = 0 -5a + 0 + -9c = 0 + 12b -5a + -9c = 0 + 12b Remove the zero: -5a + -9c = 12b Add '9c' to each side of the equation. -5a + -9c + 9c = 12b + 9c Combine like terms: -9c + 9c = 0 -5a + 0 = 12b + 9c -5a = 12b + 9c Divide each side by '-5'. a = -2.4b + -1.8c Simplifying a = -2.4b + -1.8c
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