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Simplifying 75xy4 + -30xy2z + 3xz2 = 0 Reorder the terms: -30xy2z + 75xy4 + 3xz2 = 0 Solving -30xy2z + 75xy4 + 3xz2 = 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), '3x'. 3x(-10y2z + 25y4 + z2) = 0 Factor a trinomial. 3x((5y2 + -1z)(5y2 + -1z)) = 0 Ignore the factor 3.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 '(5y2 + -1z)' equal to zero and attempt to solve: Simplifying 5y2 + -1z = 0 Solving 5y2 + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y2' to each side of the equation. 5y2 + -5y2 + -1z = 0 + -5y2 Combine like terms: 5y2 + -5y2 = 0 0 + -1z = 0 + -5y2 -1z = 0 + -5y2 Remove the zero: -1z = -5y2 Add 'z' to each side of the equation. -1z + z = -5y2 + z Combine like terms: -1z + z = 0 0 = -5y2 + z Simplifying 0 = -5y2 + z 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 '(5y2 + -1z)' equal to zero and attempt to solve: Simplifying 5y2 + -1z = 0 Solving 5y2 + -1z = 0 Move all terms containing x to the left, all other terms to the right. Add '-5y2' to each side of the equation. 5y2 + -5y2 + -1z = 0 + -5y2 Combine like terms: 5y2 + -5y2 = 0 0 + -1z = 0 + -5y2 -1z = 0 + -5y2 Remove the zero: -1z = -5y2 Add 'z' to each side of the equation. -1z + z = -5y2 + z Combine like terms: -1z + z = 0 0 = -5y2 + z Simplifying 0 = -5y2 + 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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