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Simplifying X(X + Y + Z) = 0 (X * X + Y * X + Z * X) = 0 Reorder the terms: (XY + XZ + X2) = 0 (XY + XZ + X2) = 0 Solving XY + XZ + X2 = 0 Solving for variable 'X'. Factor out the Greatest Common Factor (GCF), 'X'. X(Y + Z + X) = 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 '(Y + Z + X)' equal to zero and attempt to solve: Simplifying Y + Z + X = 0 Reorder the terms: X + Y + Z = 0 Solving X + Y + Z = 0 Move all terms containing X to the left, all other terms to the right. Add '-1Y' to each side of the equation. X + Y + -1Y + Z = 0 + -1Y Combine like terms: Y + -1Y = 0 X + 0 + Z = 0 + -1Y X + Z = 0 + -1Y Remove the zero: X + Z = -1Y Add '-1Z' to each side of the equation. X + Z + -1Z = -1Y + -1Z Combine like terms: Z + -1Z = 0 X + 0 = -1Y + -1Z X = -1Y + -1Z Simplifying X = -1Y + -1ZSolution
X = {0, -1Y + -1Z}
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