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