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Simplifying yz(xz + -1x) = xy(z2 + -1x) + -3x Reorder the terms: yz(-1x + xz) = xy(z2 + -1x) + -3x (-1x * yz + xz * yz) = xy(z2 + -1x) + -3x (-1xyz + xyz2) = xy(z2 + -1x) + -3x Reorder the terms: -1xyz + xyz2 = xy(-1x + z2) + -3x -1xyz + xyz2 = (-1x * xy + z2 * xy) + -3x Reorder the terms: -1xyz + xyz2 = (xyz2 + -1x2y) + -3x -1xyz + xyz2 = (xyz2 + -1x2y) + -3x Reorder the terms: -1xyz + xyz2 = -3x + xyz2 + -1x2y Add '-1xyz2' to each side of the equation. -1xyz + xyz2 + -1xyz2 = -3x + xyz2 + -1xyz2 + -1x2y Combine like terms: xyz2 + -1xyz2 = 0 -1xyz + 0 = -3x + xyz2 + -1xyz2 + -1x2y -1xyz = -3x + xyz2 + -1xyz2 + -1x2y Combine like terms: xyz2 + -1xyz2 = 0 -1xyz = -3x + 0 + -1x2y -1xyz = -3x + -1x2y Solving -1xyz = -3x + -1x2y Solving for variable 'x'. Reorder the terms: 3x + -1xyz + x2y = -3x + -1x2y + 3x + x2y Reorder the terms: 3x + -1xyz + x2y = -3x + 3x + -1x2y + x2y Combine like terms: -3x + 3x = 0 3x + -1xyz + x2y = 0 + -1x2y + x2y 3x + -1xyz + x2y = -1x2y + x2y Combine like terms: -1x2y + x2y = 0 3x + -1xyz + x2y = 0 Factor out the Greatest Common Factor (GCF), 'x'. x(3 + -1yz + xy) = 0Subproblem 1
Set the factor 'x' equal to zero and attempt to solve: Simplifying x = 0 Solving x = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x = 0Subproblem 2
Set the factor '(3 + -1yz + xy)' equal to zero and attempt to solve: Simplifying 3 + -1yz + xy = 0 Reorder the terms: 3 + xy + -1yz = 0 Solving 3 + xy + -1yz = 0 Move all terms containing x to the left, all other terms to the right. Add '-3' to each side of the equation. 3 + xy + -3 + -1yz = 0 + -3 Reorder the terms: 3 + -3 + xy + -1yz = 0 + -3 Combine like terms: 3 + -3 = 0 0 + xy + -1yz = 0 + -3 xy + -1yz = 0 + -3 Combine like terms: 0 + -3 = -3 xy + -1yz = -3 Add 'yz' to each side of the equation. xy + -1yz + yz = -3 + yz Combine like terms: -1yz + yz = 0 xy + 0 = -3 + yz xy = -3 + yz Divide each side by 'y'. x = -3y-1 + z Simplifying x = -3y-1 + zSolution
x = {0, -3y-1 + z}
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