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Simplifying 10(2b + c + -6a) + -8(a + -7c + 8b) = 0 Reorder the terms: 10(-6a + 2b + c) + -8(a + -7c + 8b) = 0 (-6a * 10 + 2b * 10 + c * 10) + -8(a + -7c + 8b) = 0 (-60a + 20b + 10c) + -8(a + -7c + 8b) = 0 Reorder the terms: -60a + 20b + 10c + -8(a + 8b + -7c) = 0 -60a + 20b + 10c + (a * -8 + 8b * -8 + -7c * -8) = 0 -60a + 20b + 10c + (-8a + -64b + 56c) = 0 Reorder the terms: -60a + -8a + 20b + -64b + 10c + 56c = 0 Combine like terms: -60a + -8a = -68a -68a + 20b + -64b + 10c + 56c = 0 Combine like terms: 20b + -64b = -44b -68a + -44b + 10c + 56c = 0 Combine like terms: 10c + 56c = 66c -68a + -44b + 66c = 0 Solving -68a + -44b + 66c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '44b' to each side of the equation. -68a + -44b + 44b + 66c = 0 + 44b Combine like terms: -44b + 44b = 0 -68a + 0 + 66c = 0 + 44b -68a + 66c = 0 + 44b Remove the zero: -68a + 66c = 44b Add '-66c' to each side of the equation. -68a + 66c + -66c = 44b + -66c Combine like terms: 66c + -66c = 0 -68a + 0 = 44b + -66c -68a = 44b + -66c Divide each side by '-68'. a = -0.6470588235b + 0.9705882353c Simplifying a = -0.6470588235b + 0.9705882353c
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