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