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Simplifying (7 + 6i) * x(3 + i) = 0 Reorder the terms for easier multiplication: x(7 + 6i)(3 + i) = 0 Multiply (7 + 6i) * (3 + i) x(7(3 + i) + 6i * (3 + i)) = 0 x((3 * 7 + i * 7) + 6i * (3 + i)) = 0 x((21 + 7i) + 6i * (3 + i)) = 0 x(21 + 7i + (3 * 6i + i * 6i)) = 0 x(21 + 7i + (18i + 6i2)) = 0 Combine like terms: 7i + 18i = 25i x(21 + 25i + 6i2) = 0 (21 * x + 25i * x + 6i2 * x) = 0 Reorder the terms: (25ix + 6i2x + 21x) = 0 (25ix + 6i2x + 21x) = 0 Solving 25ix + 6i2x + 21x = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'x'. x(25i + 6i2 + 21) = 0 Factor a trinomial. x((6i + 7)(i + 3)) = 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 '(6i + 7)' equal to zero and attempt to solve: Simplifying 6i + 7 = 0 Reorder the terms: 7 + 6i = 0 Solving 7 + 6i = 0 Move all terms containing i to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + 6i = 0 + -7 Combine like terms: 7 + -7 = 0 0 + 6i = 0 + -7 6i = 0 + -7 Combine like terms: 0 + -7 = -7 6i = -7 Divide each side by '6'. i = -1.166666667 Simplifying i = -1.166666667Subproblem 3
Set the factor '(i + 3)' equal to zero and attempt to solve: Simplifying i + 3 = 0 Reorder the terms: 3 + i = 0 Solving 3 + i = 0 Move all terms containing i to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + -3 + i = 0 + -3 Combine like terms: 3 + -3 = 0 0 + i = 0 + -3 i = 0 + -3 Combine like terms: 0 + -3 = -3 i = -3 Simplifying i = -3Solution
i = {-1.166666667, -3}
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