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Simplifying (2x + -3y) + 12i = (3x + 2y) * i + 8 Remove parenthesis around (2x + -3y) 2x + -3y + 12i = (3x + 2y) * i + 8 Reorder the terms: 12i + 2x + -3y = (3x + 2y) * i + 8 Reorder the terms for easier multiplication: 12i + 2x + -3y = i(3x + 2y) + 8 12i + 2x + -3y = (3x * i + 2y * i) + 8 12i + 2x + -3y = (3ix + 2iy) + 8 Reorder the terms: 12i + 2x + -3y = 8 + 3ix + 2iy Solving 12i + 2x + -3y = 8 + 3ix + 2iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-3ix' to each side of the equation. 12i + 2x + -3ix + -3y = 8 + 3ix + -3ix + 2iy Reorder the terms: 12i + -3ix + 2x + -3y = 8 + 3ix + -3ix + 2iy Combine like terms: 3ix + -3ix = 0 12i + -3ix + 2x + -3y = 8 + 0 + 2iy 12i + -3ix + 2x + -3y = 8 + 2iy Add '-2iy' to each side of the equation. 12i + -3ix + 2x + -2iy + -3y = 8 + 2iy + -2iy Reorder the terms: 12i + -3ix + -2iy + 2x + -3y = 8 + 2iy + -2iy Combine like terms: 2iy + -2iy = 0 12i + -3ix + -2iy + 2x + -3y = 8 + 0 12i + -3ix + -2iy + 2x + -3y = 8 Add '-2x' to each side of the equation. 12i + -3ix + -2iy + 2x + -2x + -3y = 8 + -2x Combine like terms: 2x + -2x = 0 12i + -3ix + -2iy + 0 + -3y = 8 + -2x 12i + -3ix + -2iy + -3y = 8 + -2x Add '3y' to each side of the equation. 12i + -3ix + -2iy + -3y + 3y = 8 + -2x + 3y Combine like terms: -3y + 3y = 0 12i + -3ix + -2iy + 0 = 8 + -2x + 3y 12i + -3ix + -2iy = 8 + -2x + 3y Reorder the terms: -8 + 12i + -3ix + -2iy + 2x + -3y = 8 + -2x + 3y + -8 + 2x + -3y Reorder the terms: -8 + 12i + -3ix + -2iy + 2x + -3y = 8 + -8 + -2x + 2x + 3y + -3y Combine like terms: 8 + -8 = 0 -8 + 12i + -3ix + -2iy + 2x + -3y = 0 + -2x + 2x + 3y + -3y -8 + 12i + -3ix + -2iy + 2x + -3y = -2x + 2x + 3y + -3y Combine like terms: -2x + 2x = 0 -8 + 12i + -3ix + -2iy + 2x + -3y = 0 + 3y + -3y -8 + 12i + -3ix + -2iy + 2x + -3y = 3y + -3y Combine like terms: 3y + -3y = 0 -8 + 12i + -3ix + -2iy + 2x + -3y = 0 The solution to this equation could not be determined.
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