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Simplifying 10(3b + c + -6a) + -8(a + -8c + 9b) = 0 Reorder the terms: 10(-6a + 3b + c) + -8(a + -8c + 9b) = 0 (-6a * 10 + 3b * 10 + c * 10) + -8(a + -8c + 9b) = 0 (-60a + 30b + 10c) + -8(a + -8c + 9b) = 0 Reorder the terms: -60a + 30b + 10c + -8(a + 9b + -8c) = 0 -60a + 30b + 10c + (a * -8 + 9b * -8 + -8c * -8) = 0 -60a + 30b + 10c + (-8a + -72b + 64c) = 0 Reorder the terms: -60a + -8a + 30b + -72b + 10c + 64c = 0 Combine like terms: -60a + -8a = -68a -68a + 30b + -72b + 10c + 64c = 0 Combine like terms: 30b + -72b = -42b -68a + -42b + 10c + 64c = 0 Combine like terms: 10c + 64c = 74c -68a + -42b + 74c = 0 Solving -68a + -42b + 74c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '42b' to each side of the equation. -68a + -42b + 42b + 74c = 0 + 42b Combine like terms: -42b + 42b = 0 -68a + 0 + 74c = 0 + 42b -68a + 74c = 0 + 42b Remove the zero: -68a + 74c = 42b Add '-74c' to each side of the equation. -68a + 74c + -74c = 42b + -74c Combine like terms: 74c + -74c = 0 -68a + 0 = 42b + -74c -68a = 42b + -74c Divide each side by '-68'. a = -0.6176470588b + 1.088235294c Simplifying a = -0.6176470588b + 1.088235294c
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