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Simplifying Y = (x + -5)(x + -1(3 + 2i))(x + (3 + -2i)) Reorder the terms: Y = (-5 + x)(x + -1(3 + 2i))(x + (3 + -2i)) Y = (-5 + x)(x + (3 * -1 + 2i * -1))(x + (3 + -2i)) Y = (-5 + x)(x + (-3 + -2i))(x + (3 + -2i)) Reorder the terms: Y = (-5 + x)(-3 + -2i + x)(x + (3 + -2i)) Remove parenthesis around (3 + -2i) Y = (-5 + x)(-3 + -2i + x)(x + 3 + -2i) Reorder the terms: Y = (-5 + x)(-3 + -2i + x)(3 + -2i + x) Multiply (-5 + x) * (-3 + -2i + x) Y = (-5(-3 + -2i + x) + x(-3 + -2i + x))(3 + -2i + x) Y = ((-3 * -5 + -2i * -5 + x * -5) + x(-3 + -2i + x))(3 + -2i + x) Y = ((15 + 10i + -5x) + x(-3 + -2i + x))(3 + -2i + x) Y = (15 + 10i + -5x + (-3 * x + -2i * x + x * x))(3 + -2i + x) Reorder the terms: Y = (15 + 10i + -5x + (-2ix + -3x + x2))(3 + -2i + x) Y = (15 + 10i + -5x + (-2ix + -3x + x2))(3 + -2i + x) Reorder the terms: Y = (15 + 10i + -2ix + -5x + -3x + x2)(3 + -2i + x) Combine like terms: -5x + -3x = -8x Y = (15 + 10i + -2ix + -8x + x2)(3 + -2i + x) Multiply (15 + 10i + -2ix + -8x + x2) * (3 + -2i + x) Y = (15(3 + -2i + x) + 10i * (3 + -2i + x) + -2ix * (3 + -2i + x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = ((3 * 15 + -2i * 15 + x * 15) + 10i * (3 + -2i + x) + -2ix * (3 + -2i + x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = ((45 + -30i + 15x) + 10i * (3 + -2i + x) + -2ix * (3 + -2i + x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + (3 * 10i + -2i * 10i + x * 10i) + -2ix * (3 + -2i + x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Reorder the terms: Y = (45 + -30i + 15x + (30i + 10ix + -20i2) + -2ix * (3 + -2i + x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + (30i + 10ix + -20i2) + -2ix * (3 + -2i + x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + (3 * -2ix + -2i * -2ix + x * -2ix) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Reorder the terms: Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + (-6ix + -2ix2 + 4i2x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + (-6ix + -2ix2 + 4i2x) + -8x * (3 + -2i + x) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + -6ix + -2ix2 + 4i2x + (3 * -8x + -2i * -8x + x * -8x) + x2(3 + -2i + x)) Reorder the terms: Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + -6ix + -2ix2 + 4i2x + (16ix + -24x + -8x2) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + -6ix + -2ix2 + 4i2x + (16ix + -24x + -8x2) + x2(3 + -2i + x)) Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + -6ix + -2ix2 + 4i2x + 16ix + -24x + -8x2 + (3 * x2 + -2i * x2 + x * x2)) Reorder the terms: Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + -6ix + -2ix2 + 4i2x + 16ix + -24x + -8x2 + (-2ix2 + 3x2 + x3)) Y = (45 + -30i + 15x + 30i + 10ix + -20i2 + -6ix + -2ix2 + 4i2x + 16ix + -24x + -8x2 + (-2ix2 + 3x2 + x3)) Reorder the terms: Y = (45 + -30i + 30i + 10ix + -6ix + 16ix + -2ix2 + -2ix2 + -20i2 + 4i2x + 15x + -24x + -8x2 + 3x2 + x3) Combine like terms: -30i + 30i = 0 Y = (45 + 0 + 10ix + -6ix + 16ix + -2ix2 + -2ix2 + -20i2 + 4i2x + 15x + -24x + -8x2 + 3x2 + x3) Y = (45 + 10ix + -6ix + 16ix + -2ix2 + -2ix2 + -20i2 + 4i2x + 15x + -24x + -8x2 + 3x2 + x3) Combine like terms: 10ix + -6ix = 4ix Y = (45 + 4ix + 16ix + -2ix2 + -2ix2 + -20i2 + 4i2x + 15x + -24x + -8x2 + 3x2 + x3) Combine like terms: 4ix + 16ix = 20ix Y = (45 + 20ix + -2ix2 + -2ix2 + -20i2 + 4i2x + 15x + -24x + -8x2 + 3x2 + x3) Combine like terms: -2ix2 + -2ix2 = -4ix2 Y = (45 + 20ix + -4ix2 + -20i2 + 4i2x + 15x + -24x + -8x2 + 3x2 + x3) Combine like terms: 15x + -24x = -9x Y = (45 + 20ix + -4ix2 + -20i2 + 4i2x + -9x + -8x2 + 3x2 + x3) Combine like terms: -8x2 + 3x2 = -5x2 Y = (45 + 20ix + -4ix2 + -20i2 + 4i2x + -9x + -5x2 + x3) Solving Y = 45 + 20ix + -4ix2 + -20i2 + 4i2x + -9x + -5x2 + x3 Solving for variable 'Y'. Move all terms containing Y to the left, all other terms to the right. Simplifying Y = 45 + 20ix + -4ix2 + -20i2 + 4i2x + -9x + -5x2 + x3
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