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Simplifying 6a + 3b + 3c + -2a + -2b + 4c = 0 Reorder the terms: 6a + -2a + 3b + -2b + 3c + 4c = 0 Combine like terms: 6a + -2a = 4a 4a + 3b + -2b + 3c + 4c = 0 Combine like terms: 3b + -2b = 1b 4a + 1b + 3c + 4c = 0 Combine like terms: 3c + 4c = 7c 4a + 1b + 7c = 0 Solving 4a + 1b + 7c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-1b' to each side of the equation. 4a + 1b + -1b + 7c = 0 + -1b Combine like terms: 1b + -1b = 0 4a + 0 + 7c = 0 + -1b 4a + 7c = 0 + -1b Remove the zero: 4a + 7c = -1b Add '-7c' to each side of the equation. 4a + 7c + -7c = -1b + -7c Combine like terms: 7c + -7c = 0 4a + 0 = -1b + -7c 4a = -1b + -7c Divide each side by '4'. a = -0.25b + -1.75c Simplifying a = -0.25b + -1.75c
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