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Simplifying 2(-6 + -9i) + -6(-6i + -9i) + 9 = 0 (-6 * 2 + -9i * 2) + -6(-6i + -9i) + 9 = 0 (-12 + -18i) + -6(-6i + -9i) + 9 = 0 Combine like terms: -6i + -9i = -15i -12 + -18i + -6(-15i) + 9 = 0 Remove parenthesis around (-15i) -12 + -18i + -6 * -15i + 9 = 0 Multiply -6 * -15 -12 + -18i + 90i + 9 = 0 Reorder the terms: -12 + 9 + -18i + 90i = 0 Combine like terms: -12 + 9 = -3 -3 + -18i + 90i = 0 Combine like terms: -18i + 90i = 72i -3 + 72i = 0 Solving -3 + 72i = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + 3 + 72i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 72i = 0 + 3 72i = 0 + 3 Combine like terms: 0 + 3 = 3 72i = 3 Divide each side by '72'. i = 0.04166666667 Simplifying i = 0.04166666667
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