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Simplifying (3a + b) + 2(b + c) + -4(c + d) = 0 Remove parenthesis around (3a + b) 3a + b + 2(b + c) + -4(c + d) = 0 3a + b + (b * 2 + c * 2) + -4(c + d) = 0 3a + b + (2b + 2c) + -4(c + d) = 0 3a + b + 2b + 2c + (c * -4 + d * -4) = 0 3a + b + 2b + 2c + (-4c + -4d) = 0 Combine like terms: b + 2b = 3b 3a + 3b + 2c + -4c + -4d = 0 Combine like terms: 2c + -4c = -2c 3a + 3b + -2c + -4d = 0 Solving 3a + 3b + -2c + -4d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 3a + 3b + -2c + -3b + -4d = 0 + -3b Reorder the terms: 3a + 3b + -3b + -2c + -4d = 0 + -3b Combine like terms: 3b + -3b = 0 3a + 0 + -2c + -4d = 0 + -3b 3a + -2c + -4d = 0 + -3b Remove the zero: 3a + -2c + -4d = -3b Add '2c' to each side of the equation. 3a + -2c + 2c + -4d = -3b + 2c Combine like terms: -2c + 2c = 0 3a + 0 + -4d = -3b + 2c 3a + -4d = -3b + 2c Add '4d' to each side of the equation. 3a + -4d + 4d = -3b + 2c + 4d Combine like terms: -4d + 4d = 0 3a + 0 = -3b + 2c + 4d 3a = -3b + 2c + 4d Divide each side by '3'. a = -1b + 0.6666666667c + 1.333333333d Simplifying a = -1b + 0.6666666667c + 1.333333333d
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