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Simplifying (2x + 3yi) + (3x + -4x) * i = (x + -2)(2y + -5) * i Reorder the terms: (3iy + 2x) + (3x + -4x) * i = (x + -2)(2y + -5) * i Remove parenthesis around (3iy + 2x) 3iy + 2x + (3x + -4x) * i = (x + -2)(2y + -5) * i Combine like terms: 3x + -4x = -1x 3iy + 2x + (-1x) * i = (x + -2)(2y + -5) * i Remove parenthesis around (-1x) 3iy + 2x + -1x * i = (x + -2)(2y + -5) * i Multiply x * i 3iy + 2x + -1ix = (x + -2)(2y + -5) * i Reorder the terms: -1ix + 3iy + 2x = (x + -2)(2y + -5) * i Reorder the terms: -1ix + 3iy + 2x = (-2 + x)(2y + -5) * i Reorder the terms: -1ix + 3iy + 2x = (-2 + x)(-5 + 2y) * i Reorder the terms for easier multiplication: -1ix + 3iy + 2x = i(-2 + x)(-5 + 2y) Multiply (-2 + x) * (-5 + 2y) -1ix + 3iy + 2x = i(-2(-5 + 2y) + x(-5 + 2y)) -1ix + 3iy + 2x = i((-5 * -2 + 2y * -2) + x(-5 + 2y)) -1ix + 3iy + 2x = i((10 + -4y) + x(-5 + 2y)) -1ix + 3iy + 2x = i(10 + -4y + (-5 * x + 2y * x)) -1ix + 3iy + 2x = i(10 + -4y + (-5x + 2xy)) Reorder the terms: -1ix + 3iy + 2x = i(10 + -5x + 2xy + -4y) -1ix + 3iy + 2x = i(10 + -5x + 2xy + -4y) -1ix + 3iy + 2x = (10 * i + -5x * i + 2xy * i + -4y * i) -1ix + 3iy + 2x = (10i + -5ix + 2ixy + -4iy) Solving -1ix + 3iy + 2x = 10i + -5ix + 2ixy + -4iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '-10i' to each side of the equation. -1ix + 3iy + -10i + 2x = 10i + -5ix + 2ixy + -10i + -4iy Reorder the terms: -10i + -1ix + 3iy + 2x = 10i + -5ix + 2ixy + -10i + -4iy Reorder the terms: -10i + -1ix + 3iy + 2x = 10i + -10i + -5ix + 2ixy + -4iy Combine like terms: 10i + -10i = 0 -10i + -1ix + 3iy + 2x = 0 + -5ix + 2ixy + -4iy -10i + -1ix + 3iy + 2x = -5ix + 2ixy + -4iy Add '5ix' to each side of the equation. -10i + -1ix + 3iy + 5ix + 2x = -5ix + 2ixy + 5ix + -4iy Reorder the terms: -10i + -1ix + 5ix + 3iy + 2x = -5ix + 2ixy + 5ix + -4iy Combine like terms: -1ix + 5ix = 4ix -10i + 4ix + 3iy + 2x = -5ix + 2ixy + 5ix + -4iy Reorder the terms: -10i + 4ix + 3iy + 2x = -5ix + 5ix + 2ixy + -4iy Combine like terms: -5ix + 5ix = 0 -10i + 4ix + 3iy + 2x = 0 + 2ixy + -4iy -10i + 4ix + 3iy + 2x = 2ixy + -4iy Add '-2ixy' to each side of the equation. -10i + 4ix + 3iy + -2ixy + 2x = 2ixy + -2ixy + -4iy Reorder the terms: -10i + 4ix + -2ixy + 3iy + 2x = 2ixy + -2ixy + -4iy Combine like terms: 2ixy + -2ixy = 0 -10i + 4ix + -2ixy + 3iy + 2x = 0 + -4iy -10i + 4ix + -2ixy + 3iy + 2x = -4iy Add '4iy' to each side of the equation. -10i + 4ix + -2ixy + 3iy + 4iy + 2x = -4iy + 4iy Combine like terms: 3iy + 4iy = 7iy -10i + 4ix + -2ixy + 7iy + 2x = -4iy + 4iy Combine like terms: -4iy + 4iy = 0 -10i + 4ix + -2ixy + 7iy + 2x = 0 Add '-2x' to each side of the equation. -10i + 4ix + -2ixy + 7iy + 2x + -2x = 0 + -2x Combine like terms: 2x + -2x = 0 -10i + 4ix + -2ixy + 7iy + 0 = 0 + -2x -10i + 4ix + -2ixy + 7iy = 0 + -2x Remove the zero: -10i + 4ix + -2ixy + 7iy = -2x Combine like terms: -2x + 2x = 0 -10i + 4ix + -2ixy + 7iy + 2x = 0 The solution to this equation could not be determined.
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