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Simplifying (3 + -2i) * x(4 + i) = 0 Reorder the terms for easier multiplication: x(3 + -2i)(4 + i) = 0 Multiply (3 + -2i) * (4 + i) x(3(4 + i) + -2i * (4 + i)) = 0 x((4 * 3 + i * 3) + -2i * (4 + i)) = 0 x((12 + 3i) + -2i * (4 + i)) = 0 x(12 + 3i + (4 * -2i + i * -2i)) = 0 x(12 + 3i + (-8i + -2i2)) = 0 Combine like terms: 3i + -8i = -5i x(12 + -5i + -2i2) = 0 (12 * x + -5i * x + -2i2 * x) = 0 Reorder the terms: (-5ix + -2i2x + 12x) = 0 (-5ix + -2i2x + 12x) = 0 Solving -5ix + -2i2x + 12x = 0 Solving for variable 'i'. Factor out the Greatest Common Factor (GCF), 'x'. x(-5i + -2i2 + 12) = 0 Factor a trinomial. x((-1i + -4)(2i + -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 '(-1i + -4)' equal to zero and attempt to solve: Simplifying -1i + -4 = 0 Reorder the terms: -4 + -1i = 0 Solving -4 + -1i = 0 Move all terms containing i to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1i = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1i = 0 + 4 -1i = 0 + 4 Combine like terms: 0 + 4 = 4 -1i = 4 Divide each side by '-1'. i = -4 Simplifying i = -4Subproblem 3
Set the factor '(2i + -3)' equal to zero and attempt to solve: Simplifying 2i + -3 = 0 Reorder the terms: -3 + 2i = 0 Solving -3 + 2i = 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 + 2i = 0 + 3 Combine like terms: -3 + 3 = 0 0 + 2i = 0 + 3 2i = 0 + 3 Combine like terms: 0 + 3 = 3 2i = 3 Divide each side by '2'. i = 1.5 Simplifying i = 1.5Solution
i = {-4, 1.5}
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