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Simplifying 6xy4 + -6xz4 = 0 Solving 6xy4 + -6xz4 = 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), '6x'. 6x(y4 + -1z4) = 0 Factor a difference between two squares. 6x((y2 + z2)(y2 + -1z2)) = 0 Factor a difference between two squares. 6x((y2 + z2)((y + z)(y + -1z))) = 0 Ignore the factor 6.Subproblem 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 '(y2 + z2)' equal to zero and attempt to solve: Simplifying y2 + z2 = 0 Solving y2 + z2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y2' to each side of the equation. y2 + -1y2 + z2 = 0 + -1y2 Combine like terms: y2 + -1y2 = 0 0 + z2 = 0 + -1y2 z2 = 0 + -1y2 Remove the zero: z2 = -1y2 Add '-1z2' to each side of the equation. z2 + -1z2 = -1y2 + -1z2 Combine like terms: z2 + -1z2 = 0 0 = -1y2 + -1z2 Simplifying 0 = -1y2 + -1z2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 3
Set the factor '(y + z)' equal to zero and attempt to solve: Simplifying y + z = 0 Solving 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. y + -1y + z = 0 + -1y Combine like terms: y + -1y = 0 0 + z = 0 + -1y z = 0 + -1y Remove the zero: z = -1y Add '-1z' to each side of the equation. z + -1z = -1y + -1z Combine like terms: z + -1z = 0 0 = -1y + -1z Simplifying 0 = -1y + -1z The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 4
Set the factor '(y + -1z)' equal to zero and attempt to solve: Simplifying y + -1z = 0 Solving y + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. y + -1y + -1z = 0 + -1y Combine like terms: y + -1y = 0 0 + -1z = 0 + -1y -1z = 0 + -1y Remove the zero: -1z = -1y Add 'z' to each side of the equation. -1z + z = -1y + z Combine like terms: -1z + z = 0 0 = -1y + z Simplifying 0 = -1y + 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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