8x^2z^2-4xz^2-12z^2=0

Solution for 8x^2z^2-4xz^2-12z^2=0 equation:

Simplifying
8x2z2 + -4xz2 + -12z2 = 0

Reorder the terms:
-4xz2 + 8x2z2 + -12z2 = 0

Solving
-4xz2 + 8x2z2 + -12z2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4z2'.
4z2(-1x + 2x2 + -3) = 0

Factor a trinomial.
4z2((2x + -3)(x + 1)) = 0

Ignore the factor 4.
Subproblem 1
Set the factor 'z2' equal to zero and attempt to solve:

Simplifying
z2 = 0

Solving
z2 = 0

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

Add '-1z2' to each side of the equation.
z2 + -1z2 = 0 + -1z2
Remove the zero:
0 = -1z2

Simplifying
0 = -1z2

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 + -3)' equal to zero and attempt to solve:

Simplifying
2x + -3 = 0

Reorder the terms:
-3 + 2x = 0

Solving
-3 + 2x = 0

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

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

Combine like terms: -3 + 3 = 0
0 + 2x = 0 + 3
2x = 0 + 3

Combine like terms: 0 + 3 = 3
2x = 3

Divide each side by '2'.
x = 1.5

Simplifying
x = 1.5
Subproblem 3
Set the factor '(x + 1)' equal to zero and attempt to solve:

Simplifying
x + 1 = 0

Reorder the terms:
1 + x = 0

Solving
1 + x = 0

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

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

Combine like terms: 1 + -1 = 0
0 + x = 0 + -1
x = 0 + -1

Combine like terms: 0 + -1 = -1
x = -1

Simplifying
x = -1
Solution
x = {1.5, -1}