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Simplifying (3x + -4)(5 + 2i) = 38 + -16yi Reorder the terms: (-4 + 3x)(5 + 2i) = 38 + -16yi Multiply (-4 + 3x) * (5 + 2i) (-4(5 + 2i) + 3x * (5 + 2i)) = 38 + -16yi ((5 * -4 + 2i * -4) + 3x * (5 + 2i)) = 38 + -16yi ((-20 + -8i) + 3x * (5 + 2i)) = 38 + -16yi (-20 + -8i + (5 * 3x + 2i * 3x)) = 38 + -16yi Reorder the terms: (-20 + -8i + (6ix + 15x)) = 38 + -16yi (-20 + -8i + (6ix + 15x)) = 38 + -16yi (-20 + -8i + 6ix + 15x) = 38 + -16yi Solving -20 + -8i + 6ix + 15x = 38 + -16iy Solving for variable 'i'. Move all terms containing i to the left, all other terms to the right. Add '16iy' to each side of the equation. -20 + -8i + 6ix + 16iy + 15x = 38 + -16iy + 16iy Combine like terms: -16iy + 16iy = 0 -20 + -8i + 6ix + 16iy + 15x = 38 + 0 -20 + -8i + 6ix + 16iy + 15x = 38 Add '20' to each side of the equation. -20 + -8i + 6ix + 16iy + 20 + 15x = 38 + 20 Reorder the terms: -20 + 20 + -8i + 6ix + 16iy + 15x = 38 + 20 Combine like terms: -20 + 20 = 0 0 + -8i + 6ix + 16iy + 15x = 38 + 20 -8i + 6ix + 16iy + 15x = 38 + 20 Combine like terms: 38 + 20 = 58 -8i + 6ix + 16iy + 15x = 58 Add '-15x' to each side of the equation. -8i + 6ix + 16iy + 15x + -15x = 58 + -15x Combine like terms: 15x + -15x = 0 -8i + 6ix + 16iy + 0 = 58 + -15x -8i + 6ix + 16iy = 58 + -15x Reorder the terms: -58 + -8i + 6ix + 16iy + 15x = 58 + -15x + -58 + 15x Reorder the terms: -58 + -8i + 6ix + 16iy + 15x = 58 + -58 + -15x + 15x Combine like terms: 58 + -58 = 0 -58 + -8i + 6ix + 16iy + 15x = 0 + -15x + 15x -58 + -8i + 6ix + 16iy + 15x = -15x + 15x Combine like terms: -15x + 15x = 0 -58 + -8i + 6ix + 16iy + 15x = 0 The solution to this equation could not be determined.
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