(4xy-5z)(3xy+11z)=0

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Solution for (4xy-5z)(3xy+11z)=0 equation: 


Simplifying
(4xy + -5z)(3xy + 11z) = 0

Multiply (4xy + -5z) * (3xy + 11z)
(4xy * (3xy + 11z) + -5z * (3xy + 11z)) = 0
((3xy * 4xy + 11z * 4xy) + -5z * (3xy + 11z)) = 0

Reorder the terms:
((44xyz + 12x2y2) + -5z * (3xy + 11z)) = 0
((44xyz + 12x2y2) + -5z * (3xy + 11z)) = 0
(44xyz + 12x2y2 + (3xy * -5z + 11z * -5z)) = 0
(44xyz + 12x2y2 + (-15xyz + -55z2)) = 0

Reorder the terms:
(44xyz + -15xyz + 12x2y2 + -55z2) = 0

Combine like terms: 44xyz + -15xyz = 29xyz
(29xyz + 12x2y2 + -55z2) = 0

Solving
29xyz + 12x2y2 + -55z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4xy + -5z)(3xy + 11z) = 0


Subproblem 1
Set the factor '(4xy + -5z)' equal to zero and attempt to solve:

Simplifying
4xy + -5z = 0

Solving
4xy + -5z = 0

Move all terms containing x to the left, all other terms to the right.

Add '5z' to each side of the equation.
4xy + -5z + 5z = 0 + 5z

Combine like terms: -5z + 5z = 0
4xy + 0 = 0 + 5z
4xy = 0 + 5z
Remove the zero:
4xy = 5z

Divide each side by '4y'.
x = 1.25y-1z

Simplifying
x = 1.25y-1z

Subproblem 2
Set the factor '(3xy + 11z)' equal to zero and attempt to solve:

Simplifying
3xy + 11z = 0

Solving
3xy + 11z = 0

Move all terms containing x to the left, all other terms to the right.

Add '-11z' to each side of the equation.
3xy + 11z + -11z = 0 + -11z

Combine like terms: 11z + -11z = 0
3xy + 0 = 0 + -11z
3xy = 0 + -11z
Remove the zero:
3xy = -11z

Divide each side by '3y'.
x = -3.666666667y-1z

Simplifying
x = -3.666666667y-1z
Solution
x = {1.25y-1z, -3.666666667y-1z}

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