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Simplifying a + 2b + -3c + -5a + -8b + -2c = 0 Reorder the terms: a + -5a + 2b + -8b + -3c + -2c = 0 Combine like terms: a + -5a = -4a -4a + 2b + -8b + -3c + -2c = 0 Combine like terms: 2b + -8b = -6b -4a + -6b + -3c + -2c = 0 Combine like terms: -3c + -2c = -5c -4a + -6b + -5c = 0 Solving -4a + -6b + -5c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '6b' to each side of the equation. -4a + -6b + 6b + -5c = 0 + 6b Combine like terms: -6b + 6b = 0 -4a + 0 + -5c = 0 + 6b -4a + -5c = 0 + 6b Remove the zero: -4a + -5c = 6b Add '5c' to each side of the equation. -4a + -5c + 5c = 6b + 5c Combine like terms: -5c + 5c = 0 -4a + 0 = 6b + 5c -4a = 6b + 5c Divide each side by '-4'. a = -1.5b + -1.25c Simplifying a = -1.5b + -1.25c
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