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Simplifying 2a + -4(a + 9b + -3c) + -1(7b + 6d) + -1d = 0 2a + (a * -4 + 9b * -4 + -3c * -4) + -1(7b + 6d) + -1d = 0 2a + (-4a + -36b + 12c) + -1(7b + 6d) + -1d = 0 2a + -4a + -36b + 12c + (7b * -1 + 6d * -1) + -1d = 0 2a + -4a + -36b + 12c + (-7b + -6d) + -1d = 0 Reorder the terms: 2a + -4a + -36b + -7b + 12c + -6d + -1d = 0 Combine like terms: 2a + -4a = -2a -2a + -36b + -7b + 12c + -6d + -1d = 0 Combine like terms: -36b + -7b = -43b -2a + -43b + 12c + -6d + -1d = 0 Combine like terms: -6d + -1d = -7d -2a + -43b + 12c + -7d = 0 Solving -2a + -43b + 12c + -7d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '43b' to each side of the equation. -2a + -43b + 12c + 43b + -7d = 0 + 43b Reorder the terms: -2a + -43b + 43b + 12c + -7d = 0 + 43b Combine like terms: -43b + 43b = 0 -2a + 0 + 12c + -7d = 0 + 43b -2a + 12c + -7d = 0 + 43b Remove the zero: -2a + 12c + -7d = 43b Add '-12c' to each side of the equation. -2a + 12c + -12c + -7d = 43b + -12c Combine like terms: 12c + -12c = 0 -2a + 0 + -7d = 43b + -12c -2a + -7d = 43b + -12c Add '7d' to each side of the equation. -2a + -7d + 7d = 43b + -12c + 7d Combine like terms: -7d + 7d = 0 -2a + 0 = 43b + -12c + 7d -2a = 43b + -12c + 7d Divide each side by '-2'. a = -21.5b + 6c + -3.5d Simplifying a = -21.5b + 6c + -3.5d
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