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Simplifying 3ix + 5i + -6 = (-2 + i) * x + 3i Reorder the terms: -6 + 5i + 3ix = (-2 + i) * x + 3i Reorder the terms for easier multiplication: -6 + 5i + 3ix = x(-2 + i) + 3i -6 + 5i + 3ix = (-2 * x + i * x) + 3i Reorder the terms: -6 + 5i + 3ix = (ix + -2x) + 3i -6 + 5i + 3ix = (ix + -2x) + 3i Reorder the terms: -6 + 5i + 3ix = 3i + ix + -2x Solving -6 + 5i + 3ix = 3i + ix + -2x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3i' to each side of the equation. -6 + 5i + -3i + 3ix = 3i + ix + -3i + -2x Combine like terms: 5i + -3i = 2i -6 + 2i + 3ix = 3i + ix + -3i + -2x Reorder the terms: -6 + 2i + 3ix = 3i + -3i + ix + -2x Combine like terms: 3i + -3i = 0 -6 + 2i + 3ix = 0 + ix + -2x -6 + 2i + 3ix = ix + -2x Add '-1ix' to each side of the equation. -6 + 2i + 3ix + -1ix = ix + -1ix + -2x Combine like terms: 3ix + -1ix = 2ix -6 + 2i + 2ix = ix + -1ix + -2x Combine like terms: ix + -1ix = 0 -6 + 2i + 2ix = 0 + -2x -6 + 2i + 2ix = -2x Add '6' to each side of the equation. -6 + 2i + 6 + 2ix = 6 + -2x Reorder the terms: -6 + 6 + 2i + 2ix = 6 + -2x Combine like terms: -6 + 6 = 0 0 + 2i + 2ix = 6 + -2x 2i + 2ix = 6 + -2x Reorder the terms: -6 + 2i + 2ix + 2x = 6 + -2x + -6 + 2x Reorder the terms: -6 + 2i + 2ix + 2x = 6 + -6 + -2x + 2x Combine like terms: 6 + -6 = 0 -6 + 2i + 2ix + 2x = 0 + -2x + 2x -6 + 2i + 2ix + 2x = -2x + 2x Combine like terms: -2x + 2x = 0 -6 + 2i + 2ix + 2x = 0 Factor out the Greatest Common Factor (GCF), '2'. 2(-3 + i + ix + x) = 0 Ignore the factor 2.Subproblem 1
Set the factor '(-3 + i + ix + x)' equal to zero and attempt to solve: Simplifying -3 + i + ix + x = 0 Solving -3 + i + ix + x = 0 Move all terms containing i to the left, all other terms to the right. Add '3' to each side of the equation. -3 + i + ix + 3 + x = 0 + 3 Reorder the terms: -3 + 3 + i + ix + x = 0 + 3 Combine like terms: -3 + 3 = 0 0 + i + ix + x = 0 + 3 i + ix + x = 0 + 3 Combine like terms: 0 + 3 = 3 i + ix + x = 3 Add '-1x' to each side of the equation. i + ix + x + -1x = 3 + -1x Combine like terms: x + -1x = 0 i + ix + 0 = 3 + -1x i + ix = 3 + -1x 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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