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Simplifying 12 + -6yi = 3x + -18i Reorder the terms: 12 + -6iy = -18i + 3x Solving 12 + -6iy = -18i + 3x Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '18i' to each side of the equation. 12 + 18i + -6iy = -18i + 18i + 3x Combine like terms: -18i + 18i = 0 12 + 18i + -6iy = 0 + 3x 12 + 18i + -6iy = 3x Add '-12' to each side of the equation. 12 + 18i + -12 + -6iy = -12 + 3x Reorder the terms: 12 + -12 + 18i + -6iy = -12 + 3x Combine like terms: 12 + -12 = 0 0 + 18i + -6iy = -12 + 3x 18i + -6iy = -12 + 3x Reorder the terms: 12 + 18i + -6iy + -3x = -12 + 3x + 12 + -3x Reorder the terms: 12 + 18i + -6iy + -3x = -12 + 12 + 3x + -3x Combine like terms: -12 + 12 = 0 12 + 18i + -6iy + -3x = 0 + 3x + -3x 12 + 18i + -6iy + -3x = 3x + -3x Combine like terms: 3x + -3x = 0 12 + 18i + -6iy + -3x = 0 Factor out the Greatest Common Factor (GCF), '3'. 3(4 + 6i + -2iy + -1x) = 0 Ignore the factor 3.Subproblem 1
Set the factor '(4 + 6i + -2iy + -1x)' equal to zero and attempt to solve: Simplifying 4 + 6i + -2iy + -1x = 0 Solving 4 + 6i + -2iy + -1x = 0 Move all terms containing i to the left, all other terms to the right. Add '-4' to each side of the equation. 4 + 6i + -2iy + -4 + -1x = 0 + -4 Reorder the terms: 4 + -4 + 6i + -2iy + -1x = 0 + -4 Combine like terms: 4 + -4 = 0 0 + 6i + -2iy + -1x = 0 + -4 6i + -2iy + -1x = 0 + -4 Combine like terms: 0 + -4 = -4 6i + -2iy + -1x = -4 Add 'x' to each side of the equation. 6i + -2iy + -1x + x = -4 + x Combine like terms: -1x + x = 0 6i + -2iy + 0 = -4 + x 6i + -2iy = -4 + x 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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