2x^2z+20xz+48z=0

Solution for 2x^2z+20xz+48z=0 equation:

Simplifying
2x2z + 20xz + 48z = 0

Reorder the terms:
20xz + 2x2z + 48z = 0

Solving
20xz + 2x2z + 48z = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2z'.
2z(10x + x2 + 24) = 0

Factor a trinomial.
2z((x + 4)(x + 6)) = 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 + 4)' equal to zero and attempt to solve:

Simplifying
x + 4 = 0

Reorder the terms:
4 + x = 0

Solving
4 + x = 0

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

Add '-4' to each side of the equation.
4 + -4 + x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + x = 0 + -4
x = 0 + -4

Combine like terms: 0 + -4 = -4
x = -4

Simplifying
x = -4
Subproblem 3
Set the factor '(x + 6)' equal to zero and attempt to solve:

Simplifying
x + 6 = 0

Reorder the terms:
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
Solution
x = {-4, -6}