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Simplifying (xy + 3z)(xy + -3z) = 9 Multiply (xy + 3z) * (xy + -3z) (xy(xy + -3z) + 3z * (xy + -3z)) = 9 ((xy * xy + -3z * xy) + 3z * (xy + -3z)) = 9 Reorder the terms: ((-3xyz + x2y2) + 3z * (xy + -3z)) = 9 ((-3xyz + x2y2) + 3z * (xy + -3z)) = 9 (-3xyz + x2y2 + (xy * 3z + -3z * 3z)) = 9 (-3xyz + x2y2 + (3xyz + -9z2)) = 9 Reorder the terms: (-3xyz + 3xyz + x2y2 + -9z2) = 9 Combine like terms: -3xyz + 3xyz = 0 (0 + x2y2 + -9z2) = 9 (x2y2 + -9z2) = 9 Solving x2y2 + -9z2 = 9 Solving for variable 'x'. Move all terms containing x to the left, all other terms to the right. Add '9z2' to each side of the equation. x2y2 + -9z2 + 9z2 = 9 + 9z2 Combine like terms: -9z2 + 9z2 = 0 x2y2 + 0 = 9 + 9z2 x2y2 = 9 + 9z2 Divide each side by 'y2'. x2 = 9y-2 + 9y-2z2 Simplifying x2 = 9y-2 + 9y-2z2 Reorder the terms: x2 + -9y-2 + -9y-2z2 = 9y-2 + -9y-2 + 9y-2z2 + -9y-2z2 Combine like terms: 9y-2 + -9y-2 = 0 x2 + -9y-2 + -9y-2z2 = 0 + 9y-2z2 + -9y-2z2 x2 + -9y-2 + -9y-2z2 = 9y-2z2 + -9y-2z2 Combine like terms: 9y-2z2 + -9y-2z2 = 0 x2 + -9y-2 + -9y-2z2 = 0 Factor out the Greatest Common Factor (GCF), 'y-2'. y-2(x2y2 + -9 + -9z2) = 0Subproblem 1
Set the factor 'y-2' equal to zero and attempt to solve: Simplifying y-2 = 0 Solving y-2 = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y-2' to each side of the equation. y-2 + -1y-2 = 0 + -1y-2 Remove the zero: 0 = -1y-2 Simplifying 0 = -1y-2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined.Subproblem 2
Set the factor '(x2y2 + -9 + -9z2)' equal to zero and attempt to solve: Simplifying x2y2 + -9 + -9z2 = 0 Reorder the terms: -9 + x2y2 + -9z2 = 0 Solving -9 + x2y2 + -9z2 = 0 Move all terms containing x to the left, all other terms to the right. Add '9' to each side of the equation. -9 + x2y2 + 9 + -9z2 = 0 + 9 Reorder the terms: -9 + 9 + x2y2 + -9z2 = 0 + 9 Combine like terms: -9 + 9 = 0 0 + x2y2 + -9z2 = 0 + 9 x2y2 + -9z2 = 0 + 9 Combine like terms: 0 + 9 = 9 x2y2 + -9z2 = 9 Add '9z2' to each side of the equation. x2y2 + -9z2 + 9z2 = 9 + 9z2 Combine like terms: -9z2 + 9z2 = 0 x2y2 + 0 = 9 + 9z2 x2y2 = 9 + 9z2 Divide each side by 'y2'. x2 = 9y-2 + 9y-2z2 Simplifying x2 = 9y-2 + 9y-2z2 The solution to this equation could not be determined. This subproblem is being ignored because a solution could not be determined. The solution to this equation could not be determined.
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