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Simplifying 2x(y + -1z) + x(y + z) = 0 (y * 2x + -1z * 2x) + x(y + z) = 0 (2xy + -2xz) + x(y + z) = 0 2xy + -2xz + (y * x + z * x) = 0 2xy + -2xz + (xy + xz) = 0 Reorder the terms: 2xy + xy + -2xz + xz = 0 Combine like terms: 2xy + xy = 3xy 3xy + -2xz + xz = 0 Combine like terms: -2xz + xz = -1xz 3xy + -1xz = 0 Solving 3xy + -1xz = 0 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Factor out the Greatest Common Factor (GCF), 'x'. x(3y + -1z) = 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 '(3y + -1z)' equal to zero and attempt to solve: Simplifying 3y + -1z = 0 Solving 3y + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add '-3y' to each side of the equation. 3y + -3y + -1z = 0 + -3y Combine like terms: 3y + -3y = 0 0 + -1z = 0 + -3y -1z = 0 + -3y Remove the zero: -1z = -3y Add 'z' to each side of the equation. -1z + z = -3y + z Combine like terms: -1z + z = 0 0 = -3y + z Simplifying 0 = -3y + z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Solution
x = {0}
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