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Simplifying (-4z3 + 9d) + -1(-12z3 + 6d) = 0 Reorder the terms: (9d + -4z3) + -1(-12z3 + 6d) = 0 Remove parenthesis around (9d + -4z3) 9d + -4z3 + -1(-12z3 + 6d) = 0 Reorder the terms: 9d + -4z3 + -1(6d + -12z3) = 0 9d + -4z3 + (6d * -1 + -12z3 * -1) = 0 9d + -4z3 + (-6d + 12z3) = 0 Reorder the terms: 9d + -6d + -4z3 + 12z3 = 0 Combine like terms: 9d + -6d = 3d 3d + -4z3 + 12z3 = 0 Combine like terms: -4z3 + 12z3 = 8z3 3d + 8z3 = 0 Solving 3d + 8z3 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-8z3' to each side of the equation. 3d + 8z3 + -8z3 = 0 + -8z3 Combine like terms: 8z3 + -8z3 = 0 3d + 0 = 0 + -8z3 3d = 0 + -8z3 Remove the zero: 3d = -8z3 Divide each side by '3'. d = -2.666666667z3 Simplifying d = -2.666666667z3
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