(6xz+3yz)(-8x-4y)=0

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Solution for (6xz+3yz)(-8x-4y)=0 equation: 


Simplifying
(6xz + 3yz)(-8x + -4y) = 0

Multiply (6xz + 3yz) * (-8x + -4y)
(6xz * (-8x + -4y) + 3yz * (-8x + -4y)) = 0
((-8x * 6xz + -4y * 6xz) + 3yz * (-8x + -4y)) = 0

Reorder the terms:
((-24xyz + -48x2z) + 3yz * (-8x + -4y)) = 0
((-24xyz + -48x2z) + 3yz * (-8x + -4y)) = 0
(-24xyz + -48x2z + (-8x * 3yz + -4y * 3yz)) = 0
(-24xyz + -48x2z + (-24xyz + -12y2z)) = 0

Reorder the terms:
(-24xyz + -24xyz + -48x2z + -12y2z) = 0

Combine like terms: -24xyz + -24xyz = -48xyz
(-48xyz + -48x2z + -12y2z) = 0

Solving
-48xyz + -48x2z + -12y2z = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '-12z'.
-12z(4xy + 4x2 + y2) = 0

Factor a trinomial.
-12z((2x + y)(2x + y)) = 0

Ignore the factor -12.

Subproblem 1
Set the factor 'z' equal to zero and attempt to solve:

Simplifying
z = 0

Solving
z = 0

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

Add '-1z' to each side of the equation.
z + -1z = 0 + -1z
Remove the zero:
0 = -1z

Simplifying
0 = -1z

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 '(2x + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y

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

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {-0.5y, -0.5y}

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