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Simplifying 4(2b + c + -3a) + -4(a + -6c + 9b) = 0 Reorder the terms: 4(-3a + 2b + c) + -4(a + -6c + 9b) = 0 (-3a * 4 + 2b * 4 + c * 4) + -4(a + -6c + 9b) = 0 (-12a + 8b + 4c) + -4(a + -6c + 9b) = 0 Reorder the terms: -12a + 8b + 4c + -4(a + 9b + -6c) = 0 -12a + 8b + 4c + (a * -4 + 9b * -4 + -6c * -4) = 0 -12a + 8b + 4c + (-4a + -36b + 24c) = 0 Reorder the terms: -12a + -4a + 8b + -36b + 4c + 24c = 0 Combine like terms: -12a + -4a = -16a -16a + 8b + -36b + 4c + 24c = 0 Combine like terms: 8b + -36b = -28b -16a + -28b + 4c + 24c = 0 Combine like terms: 4c + 24c = 28c -16a + -28b + 28c = 0 Solving -16a + -28b + 28c = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '28b' to each side of the equation. -16a + -28b + 28b + 28c = 0 + 28b Combine like terms: -28b + 28b = 0 -16a + 0 + 28c = 0 + 28b -16a + 28c = 0 + 28b Remove the zero: -16a + 28c = 28b Add '-28c' to each side of the equation. -16a + 28c + -28c = 28b + -28c Combine like terms: 28c + -28c = 0 -16a + 0 = 28b + -28c -16a = 28b + -28c Divide each side by '-16'. a = -1.75b + 1.75c Simplifying a = -1.75b + 1.75c
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