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Simplifying 3(2b + c + -8a) + -6(a + -2c + 7b) = 0 Reorder the terms: 3(-8a + 2b + c) + -6(a + -2c + 7b) = 0 (-8a * 3 + 2b * 3 + c * 3) + -6(a + -2c + 7b) = 0 (-24a + 6b + 3c) + -6(a + -2c + 7b) = 0 Reorder the terms: -24a + 6b + 3c + -6(a + 7b + -2c) = 0 -24a + 6b + 3c + (a * -6 + 7b * -6 + -2c * -6) = 0 -24a + 6b + 3c + (-6a + -42b + 12c) = 0 Reorder the terms: -24a + -6a + 6b + -42b + 3c + 12c = 0 Combine like terms: -24a + -6a = -30a -30a + 6b + -42b + 3c + 12c = 0 Combine like terms: 6b + -42b = -36b -30a + -36b + 3c + 12c = 0 Combine like terms: 3c + 12c = 15c -30a + -36b + 15c = 0 Solving -30a + -36b + 15c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '36b' to each side of the equation. -30a + -36b + 36b + 15c = 0 + 36b Combine like terms: -36b + 36b = 0 -30a + 0 + 15c = 0 + 36b -30a + 15c = 0 + 36b Remove the zero: -30a + 15c = 36b Add '-15c' to each side of the equation. -30a + 15c + -15c = 36b + -15c Combine like terms: 15c + -15c = 0 -30a + 0 = 36b + -15c -30a = 36b + -15c Divide each side by '-30'. a = -1.2b + 0.5c Simplifying a = -1.2b + 0.5c
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