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Simplifying (5 + 3i) * x(6 + -7i) = 0 Reorder the terms for easier multiplication: x(5 + 3i)(6 + -7i) = 0 Multiply (5 + 3i) * (6 + -7i) x(5(6 + -7i) + 3i * (6 + -7i)) = 0 x((6 * 5 + -7i * 5) + 3i * (6 + -7i)) = 0 x((30 + -35i) + 3i * (6 + -7i)) = 0 x(30 + -35i + (6 * 3i + -7i * 3i)) = 0 x(30 + -35i + (18i + -21i2)) = 0 Combine like terms: -35i + 18i = -17i x(30 + -17i + -21i2) = 0 (30 * x + -17i * x + -21i2 * x) = 0 Reorder the terms: (-17ix + -21i2x + 30x) = 0 (-17ix + -21i2x + 30x) = 0 Solving -17ix + -21i2x + 30x = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'x'. x(-17i + -21i2 + 30) = 0 Factor a trinomial. x((-3i + -5)(7i + -6)) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing i to the left, all other terms to the right. Add '-1x' to each side of the equation. x + -1x = 0 + -1x Remove the zero: 0 = -1x Simplifying 0 = -1x The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(-3i + -5)' equal to zero and attempt to solve: Simplifying -3i + -5 = 0 Reorder the terms: -5 + -3i = 0 Solving -5 + -3i = 0 Move all terms containing i to the left, all other terms to the right. Add '5' to each side of the equation. -5 + 5 + -3i = 0 + 5 Combine like terms: -5 + 5 = 0 0 + -3i = 0 + 5 -3i = 0 + 5 Combine like terms: 0 + 5 = 5 -3i = 5 Divide each side by '-3'. i = -1.666666667 Simplifying i = -1.666666667Subproblem 3
Set the factor '(7i + -6)' equal to zero and attempt to solve: Simplifying 7i + -6 = 0 Reorder the terms: -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 = {-1.666666667, 0.8571428571}
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