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Simplifying (x * y) = (x + 8)(y + -4) Multiply x * y (xy) = (x + 8)(y + -4) xy = (x + 8)(y + -4) Reorder the terms: xy = (8 + x)(y + -4) Reorder the terms: xy = (8 + x)(-4 + y) Multiply (8 + x) * (-4 + y) xy = (8(-4 + y) + x(-4 + y)) xy = ((-4 * 8 + y * 8) + x(-4 + y)) xy = ((-32 + 8y) + x(-4 + y)) xy = (-32 + 8y + (-4 * x + y * x)) xy = (-32 + 8y + (-4x + xy)) Reorder the terms: xy = (-32 + -4x + xy + 8y) xy = (-32 + -4x + xy + 8y) Add '-1xy' to each side of the equation. xy + -1xy = -32 + -4x + xy + -1xy + 8y Combine like terms: xy + -1xy = 0 0 = -32 + -4x + xy + -1xy + 8y Combine like terms: xy + -1xy = 0 0 = -32 + -4x + 0 + 8y 0 = -32 + -4x + 8y Solving 0 = -32 + -4x + 8y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '4x' to each side of the equation. 0 + 4x = -32 + -4x + 4x + 8y Remove the zero: 4x = -32 + -4x + 4x + 8y Combine like terms: -4x + 4x = 0 4x = -32 + 0 + 8y 4x = -32 + 8y Divide each side by '4'. x = -8 + 2y Simplifying x = -8 + 2y
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