(3x-2z)(8x+z)=

Solution for (3x-2z)(8x+z)= equation:

Simplifying
(3x + -2z)(8x + z) = 0

Multiply (3x + -2z) * (8x + z)
(3x * (8x + z) + -2z * (8x + z)) = 0
((8x * 3x + z * 3x) + -2z * (8x + z)) = 0

Reorder the terms:
((3xz + 24x2) + -2z * (8x + z)) = 0
((3xz + 24x2) + -2z * (8x + z)) = 0
(3xz + 24x2 + (8x * -2z + z * -2z)) = 0
(3xz + 24x2 + (-16xz + -2z2)) = 0

Reorder the terms:
(3xz + -16xz + 24x2 + -2z2) = 0

Combine like terms: 3xz + -16xz = -13xz
(-13xz + 24x2 + -2z2) = 0

Solving
-13xz + 24x2 + -2z2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3x + -2z)(8x + z) = 0

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

Simplifying
3x + -2z = 0

Solving
3x + -2z = 0

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

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

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

Divide each side by '3'.
x = 0.6666666667z

Simplifying
x = 0.6666666667z
Subproblem 2
Set the factor '(8x + z)' equal to zero and attempt to solve:

Simplifying
8x + z = 0

Solving
8x + z = 0

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

Add '-1z' to each side of the equation.
8x + z + -1z = 0 + -1z

Combine like terms: z + -1z = 0
8x + 0 = 0 + -1z
8x = 0 + -1z
Remove the zero:
8x = -1z

Divide each side by '8'.
x = -0.125z

Simplifying
x = -0.125z
Solution
x = {0.6666666667z, -0.125z}