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Simplifying (4 + -8i) * x(3 + i) = 0 Reorder the terms for easier multiplication: x(4 + -8i)(3 + i) = 0 Multiply (4 + -8i) * (3 + i) x(4(3 + i) + -8i * (3 + i)) = 0 x((3 * 4 + i * 4) + -8i * (3 + i)) = 0 x((12 + 4i) + -8i * (3 + i)) = 0 x(12 + 4i + (3 * -8i + i * -8i)) = 0 x(12 + 4i + (-24i + -8i2)) = 0 Combine like terms: 4i + -24i = -20i x(12 + -20i + -8i2) = 0 (12 * x + -20i * x + -8i2 * x) = 0 Reorder the terms: (-20ix + -8i2x + 12x) = 0 (-20ix + -8i2x + 12x) = 0 Solving -20ix + -8i2x + 12x = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), '4x'. 4x(-5i + -2i2 + 3) = 0 Factor a trinomial. 4x((-1i + -3)(2i + -1)) = 0 Ignore the factor 4.Subproblem 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 '(-1i + -3)' equal to zero and attempt to solve: Simplifying -1i + -3 = 0 Reorder the terms: -3 + -1i = 0 Solving -3 + -1i = 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 + -1i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + -1i = 0 + 3 -1i = 0 + 3 Combine like terms: 0 + 3 = 3 -1i = 3 Divide each side by '-1'. i = -3 Simplifying i = -3Subproblem 3
Set the factor '(2i + -1)' equal to zero and attempt to solve: Simplifying 2i + -1 = 0 Reorder the terms: -1 + 2i = 0 Solving -1 + 2i = 0 Move all terms containing i to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + 2i = 0 + 1 Combine like terms: -1 + 1 = 0 0 + 2i = 0 + 1 2i = 0 + 1 Combine like terms: 0 + 1 = 1 2i = 1 Divide each side by '2'. i = 0.5 Simplifying i = 0.5Solution
i = {-3, 0.5}
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