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Simplifying (4z3 + 9d) + -1(-12z3 + d) = 0 Reorder the terms: (9d + 4z3) + -1(-12z3 + d) = 0 Remove parenthesis around (9d + 4z3) 9d + 4z3 + -1(-12z3 + d) = 0 Reorder the terms: 9d + 4z3 + -1(d + -12z3) = 0 9d + 4z3 + (d * -1 + -12z3 * -1) = 0 9d + 4z3 + (-1d + 12z3) = 0 Reorder the terms: 9d + -1d + 4z3 + 12z3 = 0 Combine like terms: 9d + -1d = 8d 8d + 4z3 + 12z3 = 0 Combine like terms: 4z3 + 12z3 = 16z3 8d + 16z3 = 0 Solving 8d + 16z3 = 0 Solving for variable 'd'. Move all terms containing d to the left, all other terms to the right. Add '-16z3' to each side of the equation. 8d + 16z3 + -16z3 = 0 + -16z3 Combine like terms: 16z3 + -16z3 = 0 8d + 0 = 0 + -16z3 8d = 0 + -16z3 Remove the zero: 8d = -16z3 Divide each side by '8'. d = -2z3 Simplifying d = -2z3
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