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Simplifying (xy + -3z)(4xy + 11z) = 0 Multiply (xy + -3z) * (4xy + 11z) (xy(4xy + 11z) + -3z * (4xy + 11z)) = 0 ((4xy * xy + 11z * xy) + -3z * (4xy + 11z)) = 0 Reorder the terms: ((11xyz + 4x2y2) + -3z * (4xy + 11z)) = 0 ((11xyz + 4x2y2) + -3z * (4xy + 11z)) = 0 (11xyz + 4x2y2 + (4xy * -3z + 11z * -3z)) = 0 (11xyz + 4x2y2 + (-12xyz + -33z2)) = 0 Reorder the terms: (11xyz + -12xyz + 4x2y2 + -33z2) = 0 Combine like terms: 11xyz + -12xyz = -1xyz (-1xyz + 4x2y2 + -33z2) = 0 Solving -1xyz + 4x2y2 + -33z2 = 0 Solving for variable 'x'. Factor a trinomial. (xy + -3z)(4xy + 11z) = 0Subproblem 1
Set the factor '(xy + -3z)' equal to zero and attempt to solve: Simplifying xy + -3z = 0 Solving xy + -3z = 0 Move all terms containing x to the left, all other terms to the right. Add '3z' to each side of the equation. xy + -3z + 3z = 0 + 3z Combine like terms: -3z + 3z = 0 xy + 0 = 0 + 3z xy = 0 + 3z Remove the zero: xy = 3z Divide each side by 'y'. x = 3y-1z Simplifying x = 3y-1zSubproblem 2
Set the factor '(4xy + 11z)' equal to zero and attempt to solve: Simplifying 4xy + 11z = 0 Solving 4xy + 11z = 0 Move all terms containing x to the left, all other terms to the right. Add '-11z' to each side of the equation. 4xy + 11z + -11z = 0 + -11z Combine like terms: 11z + -11z = 0 4xy + 0 = 0 + -11z 4xy = 0 + -11z Remove the zero: 4xy = -11z Divide each side by '4y'. x = -2.75y-1z Simplifying x = -2.75y-1zSolution
x = {3y-1z, -2.75y-1z}
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