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Simplifying x * y = (x + -12)(y + -12) + 12 Multiply x * y xy = (x + -12)(y + -12) + 12 Reorder the terms: xy = (-12 + x)(y + -12) + 12 Reorder the terms: xy = (-12 + x)(-12 + y) + 12 Multiply (-12 + x) * (-12 + y) xy = (-12(-12 + y) + x(-12 + y)) + 12 xy = ((-12 * -12 + y * -12) + x(-12 + y)) + 12 xy = ((144 + -12y) + x(-12 + y)) + 12 xy = (144 + -12y + (-12 * x + y * x)) + 12 xy = (144 + -12y + (-12x + xy)) + 12 Reorder the terms: xy = (144 + -12x + xy + -12y) + 12 xy = (144 + -12x + xy + -12y) + 12 Reorder the terms: xy = 144 + 12 + -12x + xy + -12y Combine like terms: 144 + 12 = 156 xy = 156 + -12x + xy + -12y Add '-1xy' to each side of the equation. xy + -1xy = 156 + -12x + xy + -1xy + -12y Combine like terms: xy + -1xy = 0 0 = 156 + -12x + xy + -1xy + -12y Combine like terms: xy + -1xy = 0 0 = 156 + -12x + 0 + -12y 0 = 156 + -12x + -12y Solving 0 = 156 + -12x + -12y Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '12x' to each side of the equation. 0 + 12x = 156 + -12x + 12x + -12y Remove the zero: 12x = 156 + -12x + 12x + -12y Combine like terms: -12x + 12x = 0 12x = 156 + 0 + -12y 12x = 156 + -12y Divide each side by '12'. x = 13 + -1y Simplifying x = 13 + -1y
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