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Simplifying 6(3b + c + -3a) + -8(a + -4c + 2b) = 0 Reorder the terms: 6(-3a + 3b + c) + -8(a + -4c + 2b) = 0 (-3a * 6 + 3b * 6 + c * 6) + -8(a + -4c + 2b) = 0 (-18a + 18b + 6c) + -8(a + -4c + 2b) = 0 Reorder the terms: -18a + 18b + 6c + -8(a + 2b + -4c) = 0 -18a + 18b + 6c + (a * -8 + 2b * -8 + -4c * -8) = 0 -18a + 18b + 6c + (-8a + -16b + 32c) = 0 Reorder the terms: -18a + -8a + 18b + -16b + 6c + 32c = 0 Combine like terms: -18a + -8a = -26a -26a + 18b + -16b + 6c + 32c = 0 Combine like terms: 18b + -16b = 2b -26a + 2b + 6c + 32c = 0 Combine like terms: 6c + 32c = 38c -26a + 2b + 38c = 0 Solving -26a + 2b + 38c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-2b' to each side of the equation. -26a + 2b + -2b + 38c = 0 + -2b Combine like terms: 2b + -2b = 0 -26a + 0 + 38c = 0 + -2b -26a + 38c = 0 + -2b Remove the zero: -26a + 38c = -2b Add '-38c' to each side of the equation. -26a + 38c + -38c = -2b + -38c Combine like terms: 38c + -38c = 0 -26a + 0 = -2b + -38c -26a = -2b + -38c Divide each side by '-26'. a = 0.07692307692b + 1.461538462c Simplifying a = 0.07692307692b + 1.461538462c
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