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Simplifying 2x2y2 + 8x2yz + -10x2z2 = 0 Reorder the terms: 8x2yz + 2x2y2 + -10x2z2 = 0 Solving 8x2yz + 2x2y2 + -10x2z2 = 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), '2x2'. 2x2(4yz + y2 + -5z2) = 0 Factor a trinomial. 2x2((y + -1z)(y + 5z)) = 0 Ignore the factor 2.Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve: Simplifying x2 = 0 Solving x2 = 0 Move all terms containing x to the left, all other terms to the right. Simplifying x2 = 0 Take the square root of each side: x = {0}Subproblem 2
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.Subproblem 3
Set the factor '(y + 5z)' equal to zero and attempt to solve: Simplifying y + 5z = 0 Solving y + 5z = 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 + 5z = 0 + -1y Combine like terms: y + -1y = 0 0 + 5z = 0 + -1y 5z = 0 + -1y Remove the zero: 5z = -1y Add '-5z' to each side of the equation. 5z + -5z = -1y + -5z Combine like terms: 5z + -5z = 0 0 = -1y + -5z Simplifying 0 = -1y + -5z 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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