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Simplifying 11(-3a + 3b + -3c) + -8(3a + -6b + 3c) = 0 (-3a * 11 + 3b * 11 + -3c * 11) + -8(3a + -6b + 3c) = 0 (-33a + 33b + -33c) + -8(3a + -6b + 3c) = 0 -33a + 33b + -33c + (3a * -8 + -6b * -8 + 3c * -8) = 0 -33a + 33b + -33c + (-24a + 48b + -24c) = 0 Reorder the terms: -33a + -24a + 33b + 48b + -33c + -24c = 0 Combine like terms: -33a + -24a = -57a -57a + 33b + 48b + -33c + -24c = 0 Combine like terms: 33b + 48b = 81b -57a + 81b + -33c + -24c = 0 Combine like terms: -33c + -24c = -57c -57a + 81b + -57c = 0 Solving -57a + 81b + -57c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-81b' to each side of the equation. -57a + 81b + -81b + -57c = 0 + -81b Combine like terms: 81b + -81b = 0 -57a + 0 + -57c = 0 + -81b -57a + -57c = 0 + -81b Remove the zero: -57a + -57c = -81b Add '57c' to each side of the equation. -57a + -57c + 57c = -81b + 57c Combine like terms: -57c + 57c = 0 -57a + 0 = -81b + 57c -57a = -81b + 57c Divide each side by '-57'. a = 1.421052632b + -1c Simplifying a = 1.421052632b + -1c
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