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Simplifying y(x + y + 3xy + 8yz + w) = 0 Reorder the terms: y(w + x + 3xy + y + 8yz) = 0 (w * y + x * y + 3xy * y + y * y + 8yz * y) = 0 (wy + xy + 3xy2 + y2 + 8y2z) = 0 Solving wy + xy + 3xy2 + y2 + 8y2z = 0 Solving for variable 'w'. Move all terms containing w to the left, all other terms to the right. Add '-1xy' to each side of the equation. wy + xy + 3xy2 + y2 + -1xy + 8y2z = 0 + -1xy Reorder the terms: wy + xy + -1xy + 3xy2 + y2 + 8y2z = 0 + -1xy Combine like terms: xy + -1xy = 0 wy + 0 + 3xy2 + y2 + 8y2z = 0 + -1xy wy + 3xy2 + y2 + 8y2z = 0 + -1xy Remove the zero: wy + 3xy2 + y2 + 8y2z = -1xy Add '-3xy2' to each side of the equation. wy + 3xy2 + y2 + -3xy2 + 8y2z = -1xy + -3xy2 Reorder the terms: wy + 3xy2 + -3xy2 + y2 + 8y2z = -1xy + -3xy2 Combine like terms: 3xy2 + -3xy2 = 0 wy + 0 + y2 + 8y2z = -1xy + -3xy2 wy + y2 + 8y2z = -1xy + -3xy2 Add '-1y2' to each side of the equation. wy + y2 + -1y2 + 8y2z = -1xy + -3xy2 + -1y2 Combine like terms: y2 + -1y2 = 0 wy + 0 + 8y2z = -1xy + -3xy2 + -1y2 wy + 8y2z = -1xy + -3xy2 + -1y2 Add '-8y2z' to each side of the equation. wy + 8y2z + -8y2z = -1xy + -3xy2 + -1y2 + -8y2z Combine like terms: 8y2z + -8y2z = 0 wy + 0 = -1xy + -3xy2 + -1y2 + -8y2z wy = -1xy + -3xy2 + -1y2 + -8y2z Divide each side by 'y'. w = -1x + -3xy + -1y + -8yz Simplifying w = -1x + -3xy + -1y + -8yz
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