2x^2z+20xz+32z=0

Solution for 2x^2z+20xz+32z=0 equation:

Simplifying
2x2z + 20xz + 32z = 0

Reorder the terms:
20xz + 2x2z + 32z = 0

Solving
20xz + 2x2z + 32z = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(10x + x2 + 16) = 0

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

Ignore the factor 2.
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 '(x + 2)' equal to zero and attempt to solve:

Simplifying
x + 2 = 0

Reorder the terms:
2 + x = 0

Solving
2 + x = 0

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

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

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

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

Simplifying
x = -2
Subproblem 3
Set the factor '(x + 8)' equal to zero and attempt to solve:

Simplifying
x + 8 = 0

Reorder the terms:
8 + x = 0

Solving
8 + x = 0

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

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

Combine like terms: 8 + -8 = 0
0 + x = 0 + -8
x = 0 + -8

Combine like terms: 0 + -8 = -8
x = -8

Simplifying
x = -8
Solution
x = {-2, -8}