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Simplifying 2(4b + c + -4a) + -6(a + -2c + 6b) = 0 Reorder the terms: 2(-4a + 4b + c) + -6(a + -2c + 6b) = 0 (-4a * 2 + 4b * 2 + c * 2) + -6(a + -2c + 6b) = 0 (-8a + 8b + 2c) + -6(a + -2c + 6b) = 0 Reorder the terms: -8a + 8b + 2c + -6(a + 6b + -2c) = 0 -8a + 8b + 2c + (a * -6 + 6b * -6 + -2c * -6) = 0 -8a + 8b + 2c + (-6a + -36b + 12c) = 0 Reorder the terms: -8a + -6a + 8b + -36b + 2c + 12c = 0 Combine like terms: -8a + -6a = -14a -14a + 8b + -36b + 2c + 12c = 0 Combine like terms: 8b + -36b = -28b -14a + -28b + 2c + 12c = 0 Combine like terms: 2c + 12c = 14c -14a + -28b + 14c = 0 Solving -14a + -28b + 14c = 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. -14a + -28b + 28b + 14c = 0 + 28b Combine like terms: -28b + 28b = 0 -14a + 0 + 14c = 0 + 28b -14a + 14c = 0 + 28b Remove the zero: -14a + 14c = 28b Add '-14c' to each side of the equation. -14a + 14c + -14c = 28b + -14c Combine like terms: 14c + -14c = 0 -14a + 0 = 28b + -14c -14a = 28b + -14c Divide each side by '-14'. a = -2b + c Simplifying a = -2b + c
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