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Simplifying 3x + 12i = 27 + -3yi Reorder the terms: 12i + 3x = 27 + -3yi Solving 12i + 3x = 27 + -3iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '3iy' to each side of the equation. 12i + 3iy + 3x = 27 + -3iy + 3iy Combine like terms: -3iy + 3iy = 0 12i + 3iy + 3x = 27 + 0 12i + 3iy + 3x = 27 Add '-3x' to each side of the equation. 12i + 3iy + 3x + -3x = 27 + -3x Combine like terms: 3x + -3x = 0 12i + 3iy + 0 = 27 + -3x 12i + 3iy = 27 + -3x Reorder the terms: -27 + 12i + 3iy + 3x = 27 + -3x + -27 + 3x Reorder the terms: -27 + 12i + 3iy + 3x = 27 + -27 + -3x + 3x Combine like terms: 27 + -27 = 0 -27 + 12i + 3iy + 3x = 0 + -3x + 3x -27 + 12i + 3iy + 3x = -3x + 3x Combine like terms: -3x + 3x = 0 -27 + 12i + 3iy + 3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(-9 + 4i + iy + x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(-9 + 4i + iy + x)' equal to zero and attempt to solve: Simplifying -9 + 4i + iy + x = 0 Solving -9 + 4i + iy + x = 0 Move all terms containing i to the left, all other terms to the right. Add '9' to each side of the equation. -9 + 4i + iy + 9 + x = 0 + 9 Reorder the terms: -9 + 9 + 4i + iy + x = 0 + 9 Combine like terms: -9 + 9 = 0 0 + 4i + iy + x = 0 + 9 4i + iy + x = 0 + 9 Combine like terms: 0 + 9 = 9 4i + iy + x = 9 Add '-1x' to each side of the equation. 4i + iy + x + -1x = 9 + -1x Combine like terms: x + -1x = 0 4i + iy + 0 = 9 + -1x 4i + iy = 9 + -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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