4x^2z+44xz+96z=0

Solution for 4x^2z+44xz+96z=0 equation:

Simplifying
4x2z + 44xz + 96z = 0

Reorder the terms:
44xz + 4x2z + 96z = 0

Solving
44xz + 4x2z + 96z = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4z'.
4z(11x + x2 + 24) = 0

Factor a trinomial.
4z((x + 3)(x + 8)) = 0

Ignore the factor 4.
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 + 3)' equal to zero and attempt to solve:

Simplifying
x + 3 = 0

Reorder the terms:
3 + x = 0

Solving
3 + x = 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 + x = 0 + -3

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

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

Simplifying
x = -3
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 = {-3, -8}