(4xy-5z)(3xy+9z)=

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Solution for (4xy-5z)(3xy+9z)= equation: 


Simplifying
(4xy + -5z)(3xy + 9z) = 0

Multiply (4xy + -5z) * (3xy + 9z)
(4xy * (3xy + 9z) + -5z * (3xy + 9z)) = 0
((3xy * 4xy + 9z * 4xy) + -5z * (3xy + 9z)) = 0

Reorder the terms:
((36xyz + 12x2y2) + -5z * (3xy + 9z)) = 0
((36xyz + 12x2y2) + -5z * (3xy + 9z)) = 0
(36xyz + 12x2y2 + (3xy * -5z + 9z * -5z)) = 0
(36xyz + 12x2y2 + (-15xyz + -45z2)) = 0

Reorder the terms:
(36xyz + -15xyz + 12x2y2 + -45z2) = 0

Combine like terms: 36xyz + -15xyz = 21xyz
(21xyz + 12x2y2 + -45z2) = 0

Solving
21xyz + 12x2y2 + -45z2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(7xyz + 4x2y2 + -15z2) = 0

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

Ignore the factor 3.

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 '(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-1z
Solution
x = {1.25y-1z, -3y-1z}

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