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Simplifying x(x + -2 + -3i)(x + -1) = 0 Reorder the terms: x(-2 + -3i + x)(x + -1) = 0 Reorder the terms: x(-2 + -3i + x)(-1 + x) = 0 Multiply (-2 + -3i + x) * (-1 + x) x(-2(-1 + x) + -3i * (-1 + x) + x(-1 + x)) = 0 x((-1 * -2 + x * -2) + -3i * (-1 + x) + x(-1 + x)) = 0 x((2 + -2x) + -3i * (-1 + x) + x(-1 + x)) = 0 x(2 + -2x + (-1 * -3i + x * -3i) + x(-1 + x)) = 0 x(2 + -2x + (3i + -3ix) + x(-1 + x)) = 0 x(2 + -2x + 3i + -3ix + (-1 * x + x * x)) = 0 x(2 + -2x + 3i + -3ix + (-1x + x2)) = 0 Reorder the terms: x(2 + 3i + -3ix + -2x + -1x + x2) = 0 Combine like terms: -2x + -1x = -3x x(2 + 3i + -3ix + -3x + x2) = 0 (2 * x + 3i * x + -3ix * x + -3x * x + x2 * x) = 0 Reorder the terms: (3ix + -3ix2 + 2x + -3x2 + x3) = 0 (3ix + -3ix2 + 2x + -3x2 + x3) = 0 Solving 3ix + -3ix2 + 2x + -3x2 + x3 = 0 Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-2x' to each side of the equation. 3ix + -3ix2 + 2x + -3x2 + -2x + x3 = 0 + -2x Reorder the terms: 3ix + -3ix2 + 2x + -2x + -3x2 + x3 = 0 + -2x Combine like terms: 2x + -2x = 0 3ix + -3ix2 + 0 + -3x2 + x3 = 0 + -2x 3ix + -3ix2 + -3x2 + x3 = 0 + -2x Remove the zero: 3ix + -3ix2 + -3x2 + x3 = -2x Add '3x2' to each side of the equation. 3ix + -3ix2 + -3x2 + 3x2 + x3 = -2x + 3x2 Combine like terms: -3x2 + 3x2 = 0 3ix + -3ix2 + 0 + x3 = -2x + 3x2 3ix + -3ix2 + x3 = -2x + 3x2 Add '-1x3' to each side of the equation. 3ix + -3ix2 + x3 + -1x3 = -2x + 3x2 + -1x3 Combine like terms: x3 + -1x3 = 0 3ix + -3ix2 + 0 = -2x + 3x2 + -1x3 3ix + -3ix2 = -2x + 3x2 + -1x3 Reorder the terms: 3ix + -3ix2 + 2x + -3x2 + x3 = -2x + 2x + 3x2 + -3x2 + -1x3 + x3 Combine like terms: -2x + 2x = 0 3ix + -3ix2 + 2x + -3x2 + x3 = 0 + 3x2 + -3x2 + -1x3 + x3 3ix + -3ix2 + 2x + -3x2 + x3 = 3x2 + -3x2 + -1x3 + x3 Combine like terms: 3x2 + -3x2 = 0 3ix + -3ix2 + 2x + -3x2 + x3 = 0 + -1x3 + x3 3ix + -3ix2 + 2x + -3x2 + x3 = -1x3 + x3 Combine like terms: -1x3 + x3 = 0 3ix + -3ix2 + 2x + -3x2 + x3 = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(3i + -3ix + 2 + -3x + x2) = 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 + -3ix + 2 + -3x + x2)' equal to zero and attempt to solve: Simplifying 3i + -3ix + 2 + -3x + x2 = 0 Reorder the terms: 2 + 3i + -3ix + -3x + x2 = 0 Solving 2 + 3i + -3ix + -3x + x2 = 0 Move all terms containing i to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + 3i + -3ix + -3x + -2 + x2 = 0 + -2 Reorder the terms: 2 + -2 + 3i + -3ix + -3x + x2 = 0 + -2 Combine like terms: 2 + -2 = 0 0 + 3i + -3ix + -3x + x2 = 0 + -2 3i + -3ix + -3x + x2 = 0 + -2 Combine like terms: 0 + -2 = -2 3i + -3ix + -3x + x2 = -2 Add '3x' to each side of the equation. 3i + -3ix + -3x + 3x + x2 = -2 + 3x Combine like terms: -3x + 3x = 0 3i + -3ix + 0 + x2 = -2 + 3x 3i + -3ix + x2 = -2 + 3x Add '-1x2' to each side of the equation. 3i + -3ix + x2 + -1x2 = -2 + 3x + -1x2 Combine like terms: x2 + -1x2 = 0 3i + -3ix + 0 = -2 + 3x + -1x2 3i + -3ix = -2 + 3x + -1x2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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