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Simplifying y = (x + 3 + 6i)(x + 3 + -6i) Reorder the terms: y = (3 + 6i + x)(x + 3 + -6i) Reorder the terms: y = (3 + 6i + x)(3 + -6i + x) Multiply (3 + 6i + x) * (3 + -6i + x) y = (3(3 + -6i + x) + 6i * (3 + -6i + x) + x(3 + -6i + x)) y = ((3 * 3 + -6i * 3 + x * 3) + 6i * (3 + -6i + x) + x(3 + -6i + x)) y = ((9 + -18i + 3x) + 6i * (3 + -6i + x) + x(3 + -6i + x)) y = (9 + -18i + 3x + (3 * 6i + -6i * 6i + x * 6i) + x(3 + -6i + x)) Reorder the terms: y = (9 + -18i + 3x + (18i + 6ix + -36i2) + x(3 + -6i + x)) y = (9 + -18i + 3x + (18i + 6ix + -36i2) + x(3 + -6i + x)) y = (9 + -18i + 3x + 18i + 6ix + -36i2 + (3 * x + -6i * x + x * x)) Reorder the terms: y = (9 + -18i + 3x + 18i + 6ix + -36i2 + (-6ix + 3x + x2)) y = (9 + -18i + 3x + 18i + 6ix + -36i2 + (-6ix + 3x + x2)) Reorder the terms: y = (9 + -18i + 18i + 6ix + -6ix + -36i2 + 3x + 3x + x2) Combine like terms: -18i + 18i = 0 y = (9 + 0 + 6ix + -6ix + -36i2 + 3x + 3x + x2) y = (9 + 6ix + -6ix + -36i2 + 3x + 3x + x2) Combine like terms: 6ix + -6ix = 0 y = (9 + 0 + -36i2 + 3x + 3x + x2) y = (9 + -36i2 + 3x + 3x + x2) Combine like terms: 3x + 3x = 6x y = (9 + -36i2 + 6x + x2) Solving y = 9 + -36i2 + 6x + x2 Solving for variable 'y'. Move all terms containing y to the left, all other terms to the right. Simplifying y = 9 + -36i2 + 6x + x2
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