(3xy+2z)(2xy-3z)=

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Solution for (3xy+2z)(2xy-3z)= equation: 


Simplifying
(3xy + 2z)(2xy + -3z) = 0

Multiply (3xy + 2z) * (2xy + -3z)
(3xy * (2xy + -3z) + 2z * (2xy + -3z)) = 0
((2xy * 3xy + -3z * 3xy) + 2z * (2xy + -3z)) = 0

Reorder the terms:
((-9xyz + 6x2y2) + 2z * (2xy + -3z)) = 0
((-9xyz + 6x2y2) + 2z * (2xy + -3z)) = 0
(-9xyz + 6x2y2 + (2xy * 2z + -3z * 2z)) = 0
(-9xyz + 6x2y2 + (4xyz + -6z2)) = 0

Reorder the terms:
(-9xyz + 4xyz + 6x2y2 + -6z2) = 0

Combine like terms: -9xyz + 4xyz = -5xyz
(-5xyz + 6x2y2 + -6z2) = 0

Solving
-5xyz + 6x2y2 + -6z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(2xy + -3z)(3xy + 2z) = 0


Subproblem 1
Set the factor '(2xy + -3z)' equal to zero and attempt to solve:

Simplifying
2xy + -3z = 0

Solving
2xy + -3z = 0

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

Add '3z' to each side of the equation.
2xy + -3z + 3z = 0 + 3z

Combine like terms: -3z + 3z = 0
2xy + 0 = 0 + 3z
2xy = 0 + 3z
Remove the zero:
2xy = 3z

Divide each side by '2y'.
x = 1.5y-1z

Simplifying
x = 1.5y-1z

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

Simplifying
3xy + 2z = 0

Solving
3xy + 2z = 0

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

Add '-2z' to each side of the equation.
3xy + 2z + -2z = 0 + -2z

Combine like terms: 2z + -2z = 0
3xy + 0 = 0 + -2z
3xy = 0 + -2z
Remove the zero:
3xy = -2z

Divide each side by '3y'.
x = -0.6666666667y-1z

Simplifying
x = -0.6666666667y-1z
Solution
x = {1.5y-1z, -0.6666666667y-1z}

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