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Simplifying (3a + 3b + -1c) + -1(-3b + 3c + 3d) = 0 Remove parenthesis around (3a + 3b + -1c) 3a + 3b + -1c + -1(-3b + 3c + 3d) = 0 3a + 3b + -1c + (-3b * -1 + 3c * -1 + 3d * -1) = 0 3a + 3b + -1c + (3b + -3c + -3d) = 0 Reorder the terms: 3a + 3b + 3b + -1c + -3c + -3d = 0 Combine like terms: 3b + 3b = 6b 3a + 6b + -1c + -3c + -3d = 0 Combine like terms: -1c + -3c = -4c 3a + 6b + -4c + -3d = 0 Solving 3a + 6b + -4c + -3d = 0 Solving for variable 'a'. Move all terms containing a to the left, all other terms to the right. Add '-6b' to each side of the equation. 3a + 6b + -4c + -6b + -3d = 0 + -6b Reorder the terms: 3a + 6b + -6b + -4c + -3d = 0 + -6b Combine like terms: 6b + -6b = 0 3a + 0 + -4c + -3d = 0 + -6b 3a + -4c + -3d = 0 + -6b Remove the zero: 3a + -4c + -3d = -6b Add '4c' to each side of the equation. 3a + -4c + 4c + -3d = -6b + 4c Combine like terms: -4c + 4c = 0 3a + 0 + -3d = -6b + 4c 3a + -3d = -6b + 4c Add '3d' to each side of the equation. 3a + -3d + 3d = -6b + 4c + 3d Combine like terms: -3d + 3d = 0 3a + 0 = -6b + 4c + 3d 3a = -6b + 4c + 3d Divide each side by '3'. a = -2b + 1.333333333c + d Simplifying a = -2b + 1.333333333c + d
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