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Simplifying y = (x + 3)(x + 3)(x + -5 + -3i)(x + -5 + 3i) Reorder the terms: y = (3 + x)(x + 3)(x + -5 + -3i)(x + -5 + 3i) Reorder the terms: y = (3 + x)(3 + x)(x + -5 + -3i)(x + -5 + 3i) Reorder the terms: y = (3 + x)(3 + x)(-5 + -3i + x)(x + -5 + 3i) Reorder the terms: y = (3 + x)(3 + x)(-5 + -3i + x)(-5 + 3i + x) Multiply (3 + x) * (3 + x) y = (3(3 + x) + x(3 + x))(-5 + -3i + x)(-5 + 3i + x) y = ((3 * 3 + x * 3) + x(3 + x))(-5 + -3i + x)(-5 + 3i + x) y = ((9 + 3x) + x(3 + x))(-5 + -3i + x)(-5 + 3i + x) y = (9 + 3x + (3 * x + x * x))(-5 + -3i + x)(-5 + 3i + x) y = (9 + 3x + (3x + x2))(-5 + -3i + x)(-5 + 3i + x) Combine like terms: 3x + 3x = 6x y = (9 + 6x + x2)(-5 + -3i + x)(-5 + 3i + x) Multiply (9 + 6x + x2) * (-5 + -3i + x) y = (9(-5 + -3i + x) + 6x * (-5 + -3i + x) + x2(-5 + -3i + x))(-5 + 3i + x) y = ((-5 * 9 + -3i * 9 + x * 9) + 6x * (-5 + -3i + x) + x2(-5 + -3i + x))(-5 + 3i + x) y = ((-45 + -27i + 9x) + 6x * (-5 + -3i + x) + x2(-5 + -3i + x))(-5 + 3i + x) y = (-45 + -27i + 9x + (-5 * 6x + -3i * 6x + x * 6x) + x2(-5 + -3i + x))(-5 + 3i + x) Reorder the terms: y = (-45 + -27i + 9x + (-18ix + -30x + 6x2) + x2(-5 + -3i + x))(-5 + 3i + x) y = (-45 + -27i + 9x + (-18ix + -30x + 6x2) + x2(-5 + -3i + x))(-5 + 3i + x) y = (-45 + -27i + 9x + -18ix + -30x + 6x2 + (-5 * x2 + -3i * x2 + x * x2))(-5 + 3i + x) Reorder the terms: y = (-45 + -27i + 9x + -18ix + -30x + 6x2 + (-3ix2 + -5x2 + x3))(-5 + 3i + x) y = (-45 + -27i + 9x + -18ix + -30x + 6x2 + (-3ix2 + -5x2 + x3))(-5 + 3i + x) Reorder the terms: y = (-45 + -27i + -18ix + -3ix2 + 9x + -30x + 6x2 + -5x2 + x3)(-5 + 3i + x) Combine like terms: 9x + -30x = -21x y = (-45 + -27i + -18ix + -3ix2 + -21x + 6x2 + -5x2 + x3)(-5 + 3i + x) Combine like terms: 6x2 + -5x2 = 1x2 y = (-45 + -27i + -18ix + -3ix2 + -21x + 1x2 + x3)(-5 + 3i + x) Multiply (-45 + -27i + -18ix + -3ix2 + -21x + 1x2 + x3) * (-5 + 3i + x) y = (-45(-5 + 3i + x) + -27i * (-5 + 3i + x) + -18ix * (-5 + 3i + x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = ((-5 * -45 + 3i * -45 + x * -45) + -27i * (-5 + 3i + x) + -18ix * (-5 + 3i + x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = ((225 + -135i + -45x) + -27i * (-5 + 3i + x) + -18ix * (-5 + 3i + x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + (-5 * -27i + 3i * -27i + x * -27i) + -18ix * (-5 + 3i + x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) Reorder the terms: y = (225 + -135i + -45x + (135i + -27ix + -81i2) + -18ix * (-5 + 3i + x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + (135i + -27ix + -81i2) + -18ix * (-5 + 3i + x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + (-5 * -18ix + 3i * -18ix + x * -18ix) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) Reorder the terms: y = (225 + -135i + -45x + 135i + -27ix + -81i2 + (90ix + -18ix2 + -54i2x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + (90ix + -18ix2 + -54i2x) + -3ix2 * (-5 + 3i + x) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + (-5 * -3ix2 + 3i * -3ix2 + x * -3ix2) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) Reorder the terms: y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + (15ix2 + -3ix3 + -9i2x2) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + (15ix2 + -3ix3 + -9i2x2) + -21x * (-5 + 3i + x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + (-5 * -21x + 3i * -21x + x * -21x) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) Reorder the terms: y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + (-63ix + 105x + -21x2) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + (-63ix + 105x + -21x2) + 1x2 * (-5 + 3i + x) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + -63ix + 105x + -21x2 + (-5 * 1x2 + 3i * 1x2 + x * 1x2) + x3(-5 + 3i + x)) Reorder the terms: y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + -63ix + 105x + -21x2 + (3ix2 + -5x2 + 1x3) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + -63ix + 105x + -21x2 + (3ix2 + -5x2 + 1x3) + x3(-5 + 3i + x)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + -63ix + 105x + -21x2 + 3ix2 + -5x2 + 1x3 + (-5 * x3 + 3i * x3 + x * x3)) Reorder the terms: y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + -63ix + 105x + -21x2 + 3ix2 + -5x2 + 1x3 + (3ix3 + -5x3 + x4)) y = (225 + -135i + -45x + 135i + -27ix + -81i2 + 90ix + -18ix2 + -54i2x + 15ix2 + -3ix3 + -9i2x2 + -63ix + 105x + -21x2 + 3ix2 + -5x2 + 1x3 + (3ix3 + -5x3 + x4)) Reorder the terms: y = (225 + -135i + 135i + -27ix + 90ix + -63ix + -18ix2 + 15ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -135i + 135i = 0 y = (225 + 0 + -27ix + 90ix + -63ix + -18ix2 + 15ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) y = (225 + -27ix + 90ix + -63ix + -18ix2 + 15ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -27ix + 90ix = 63ix y = (225 + 63ix + -63ix + -18ix2 + 15ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: 63ix + -63ix = 0 y = (225 + 0 + -18ix2 + 15ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) y = (225 + -18ix2 + 15ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -18ix2 + 15ix2 = -3ix2 y = (225 + -3ix2 + 3ix2 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -3ix2 + 3ix2 = 0 y = (225 + 0 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) y = (225 + -3ix3 + 3ix3 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -3ix3 + 3ix3 = 0 y = (225 + 0 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) y = (225 + -81i2 + -54i2x + -9i2x2 + -45x + 105x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -45x + 105x = 60x y = (225 + -81i2 + -54i2x + -9i2x2 + 60x + -21x2 + -5x2 + 1x3 + -5x3 + x4) Combine like terms: -21x2 + -5x2 = -26x2 y = (225 + -81i2 + -54i2x + -9i2x2 + 60x + -26x2 + 1x3 + -5x3 + x4) Combine like terms: 1x3 + -5x3 = -4x3 y = (225 + -81i2 + -54i2x + -9i2x2 + 60x + -26x2 + -4x3 + x4) Solving y = 225 + -81i2 + -54i2x + -9i2x2 + 60x + -26x2 + -4x3 + x4 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 225 + -81i2 + -54i2x + -9i2x2 + 60x + -26x2 + -4x3 + x4
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