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Simplifying (3i + -2)(7i + -6) = 0 Reorder the terms: (-2 + 3i)(7i + -6) = 0 Reorder the terms: (-2 + 3i)(-6 + 7i) = 0 Multiply (-2 + 3i) * (-6 + 7i) (-2(-6 + 7i) + 3i * (-6 + 7i)) = 0 ((-6 * -2 + 7i * -2) + 3i * (-6 + 7i)) = 0 ((12 + -14i) + 3i * (-6 + 7i)) = 0 (12 + -14i + (-6 * 3i + 7i * 3i)) = 0 (12 + -14i + (-18i + 21i2)) = 0 Combine like terms: -14i + -18i = -32i (12 + -32i + 21i2) = 0 Solving 12 + -32i + 21i2 = 0 Solving for variable 'i'. Factor a trinomial. (2 + -3i)(6 + -7i) = 0Subproblem 1
Set the factor '(2 + -3i)' equal to zero and attempt to solve: Simplifying 2 + -3i = 0 Solving 2 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + -3i = 0 + -2 Combine like terms: 2 + -2 = 0 0 + -3i = 0 + -2 -3i = 0 + -2 Combine like terms: 0 + -2 = -2 -3i = -2 Divide each side by '-3'. i = 0.6666666667 Simplifying i = 0.6666666667Subproblem 2
Set the factor '(6 + -7i)' equal to zero and attempt to solve: Simplifying 6 + -7i = 0 Solving 6 + -7i = 0 Move all terms containing i to the left, all other terms to the right. Add '-6' to each side of the equation. 6 + -6 + -7i = 0 + -6 Combine like terms: 6 + -6 = 0 0 + -7i = 0 + -6 -7i = 0 + -6 Combine like terms: 0 + -6 = -6 -7i = -6 Divide each side by '-7'. i = 0.8571428571 Simplifying i = 0.8571428571Solution
i = {0.6666666667, 0.8571428571}
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