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Simplifying 3(-4a + c + 4b) + -4(2c + b + -6a) = 0 Reorder the terms: 3(-4a + 4b + c) + -4(2c + b + -6a) = 0 (-4a * 3 + 4b * 3 + c * 3) + -4(2c + b + -6a) = 0 (-12a + 12b + 3c) + -4(2c + b + -6a) = 0 Reorder the terms: -12a + 12b + 3c + -4(-6a + b + 2c) = 0 -12a + 12b + 3c + (-6a * -4 + b * -4 + 2c * -4) = 0 -12a + 12b + 3c + (24a + -4b + -8c) = 0 Reorder the terms: -12a + 24a + 12b + -4b + 3c + -8c = 0 Combine like terms: -12a + 24a = 12a 12a + 12b + -4b + 3c + -8c = 0 Combine like terms: 12b + -4b = 8b 12a + 8b + 3c + -8c = 0 Combine like terms: 3c + -8c = -5c 12a + 8b + -5c = 0 Solving 12a + 8b + -5c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-8b' to each side of the equation. 12a + 8b + -8b + -5c = 0 + -8b Combine like terms: 8b + -8b = 0 12a + 0 + -5c = 0 + -8b 12a + -5c = 0 + -8b Remove the zero: 12a + -5c = -8b Add '5c' to each side of the equation. 12a + -5c + 5c = -8b + 5c Combine like terms: -5c + 5c = 0 12a + 0 = -8b + 5c 12a = -8b + 5c Divide each side by '12'. a = -0.6666666667b + 0.4166666667c Simplifying a = -0.6666666667b + 0.4166666667c
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