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Simplifying x(-1cyz + -1 + xz + -1) + y(-1cxz + -1 + yz + -1) + -1z = 0 Reorder the terms: x(-1 + -1 + -1cyz + xz) + y(-1cxz + -1 + yz + -1) + -1z = 0 Combine like terms: -1 + -1 = -2 x(-2 + -1cyz + xz) + y(-1cxz + -1 + yz + -1) + -1z = 0 (-2 * x + -1cyz * x + xz * x) + y(-1cxz + -1 + yz + -1) + -1z = 0 Reorder the terms: (-1cxyz + -2x + x2z) + y(-1cxz + -1 + yz + -1) + -1z = 0 (-1cxyz + -2x + x2z) + y(-1cxz + -1 + yz + -1) + -1z = 0 Reorder the terms: -1cxyz + -2x + x2z + y(-1 + -1 + -1cxz + yz) + -1z = 0 Combine like terms: -1 + -1 = -2 -1cxyz + -2x + x2z + y(-2 + -1cxz + yz) + -1z = 0 -1cxyz + -2x + x2z + (-2 * y + -1cxz * y + yz * y) + -1z = 0 Reorder the terms: -1cxyz + -2x + x2z + (-1cxyz + -2y + y2z) + -1z = 0 -1cxyz + -2x + x2z + (-1cxyz + -2y + y2z) + -1z = 0 Reorder the terms: -1cxyz + -1cxyz + -2x + x2z + -2y + y2z + -1z = 0 Combine like terms: -1cxyz + -1cxyz = -2cxyz -2cxyz + -2x + x2z + -2y + y2z + -1z = 0 Solving -2cxyz + -2x + x2z + -2y + y2z + -1z = 0 Solving for variable 'c'. Move all terms containing c to the left, all other terms to the right. Add '2x' to each side of the equation. -2cxyz + -2x + x2z + -2y + y2z + 2x + -1z = 0 + 2x Reorder the terms: -2cxyz + -2x + 2x + x2z + -2y + y2z + -1z = 0 + 2x Combine like terms: -2x + 2x = 0 -2cxyz + 0 + x2z + -2y + y2z + -1z = 0 + 2x -2cxyz + x2z + -2y + y2z + -1z = 0 + 2x Remove the zero: -2cxyz + x2z + -2y + y2z + -1z = 2x Add '-1x2z' to each side of the equation. -2cxyz + x2z + -2y + y2z + -1x2z + -1z = 2x + -1x2z Reorder the terms: -2cxyz + x2z + -1x2z + -2y + y2z + -1z = 2x + -1x2z Combine like terms: x2z + -1x2z = 0 -2cxyz + 0 + -2y + y2z + -1z = 2x + -1x2z -2cxyz + -2y + y2z + -1z = 2x + -1x2z Add '2y' to each side of the equation. -2cxyz + -2y + y2z + 2y + -1z = 2x + -1x2z + 2y Reorder the terms: -2cxyz + -2y + 2y + y2z + -1z = 2x + -1x2z + 2y Combine like terms: -2y + 2y = 0 -2cxyz + 0 + y2z + -1z = 2x + -1x2z + 2y -2cxyz + y2z + -1z = 2x + -1x2z + 2y Add '-1y2z' to each side of the equation. -2cxyz + y2z + -1y2z + -1z = 2x + -1x2z + 2y + -1y2z Combine like terms: y2z + -1y2z = 0 -2cxyz + 0 + -1z = 2x + -1x2z + 2y + -1y2z -2cxyz + -1z = 2x + -1x2z + 2y + -1y2z Add 'z' to each side of the equation. -2cxyz + -1z + z = 2x + -1x2z + 2y + -1y2z + z Combine like terms: -1z + z = 0 -2cxyz + 0 = 2x + -1x2z + 2y + -1y2z + z -2cxyz = 2x + -1x2z + 2y + -1y2z + z Divide each side by '-2xyz'. c = -1y-1z-1 + 0.5xy-1 + -1x-1z-1 + 0.5x-1y + -0.5x-1y-1 Simplifying c = -1y-1z-1 + 0.5xy-1 + -1x-1z-1 + 0.5x-1y + -0.5x-1y-1 Reorder the terms: c = -0.5x-1y-1 + 0.5x-1y + -1x-1z-1 + 0.5xy-1 + -1y-1z-1
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