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Simplifying -6(3a + 5b) + -3(6a + -8c) = 0 (3a * -6 + 5b * -6) + -3(6a + -8c) = 0 (-18a + -30b) + -3(6a + -8c) = 0 -18a + -30b + (6a * -3 + -8c * -3) = 0 -18a + -30b + (-18a + 24c) = 0 Reorder the terms: -18a + -18a + -30b + 24c = 0 Combine like terms: -18a + -18a = -36a -36a + -30b + 24c = 0 Solving -36a + -30b + 24c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '30b' to each side of the equation. -36a + -30b + 30b + 24c = 0 + 30b Combine like terms: -30b + 30b = 0 -36a + 0 + 24c = 0 + 30b -36a + 24c = 0 + 30b Remove the zero: -36a + 24c = 30b Add '-24c' to each side of the equation. -36a + 24c + -24c = 30b + -24c Combine like terms: 24c + -24c = 0 -36a + 0 = 30b + -24c -36a = 30b + -24c Divide each side by '-36'. a = -0.8333333333b + 0.6666666667c Simplifying a = -0.8333333333b + 0.6666666667c
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