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Simplifying (8a + 2b + 5c) + -1(2a + b + c) = 0 Remove parenthesis around (8a + 2b + 5c) 8a + 2b + 5c + -1(2a + b + c) = 0 8a + 2b + 5c + (2a * -1 + b * -1 + c * -1) = 0 8a + 2b + 5c + (-2a + -1b + -1c) = 0 Reorder the terms: 8a + -2a + 2b + -1b + 5c + -1c = 0 Combine like terms: 8a + -2a = 6a 6a + 2b + -1b + 5c + -1c = 0 Combine like terms: 2b + -1b = 1b 6a + 1b + 5c + -1c = 0 Combine like terms: 5c + -1c = 4c 6a + 1b + 4c = 0 Solving 6a + 1b + 4c = 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. 6a + 1b + -1b + 4c = 0 + -1b Combine like terms: 1b + -1b = 0 6a + 0 + 4c = 0 + -1b 6a + 4c = 0 + -1b Remove the zero: 6a + 4c = -1b Add '-4c' to each side of the equation. 6a + 4c + -4c = -1b + -4c Combine like terms: 4c + -4c = 0 6a + 0 = -1b + -4c 6a = -1b + -4c Divide each side by '6'. a = -0.1666666667b + -0.6666666667c Simplifying a = -0.1666666667b + -0.6666666667c
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