(z-8)x(z+5)=0

Solution for (z-8)x(z+5)=0 equation:

Simplifying
(z + -8) * x(z + 5) = 0

Reorder the terms:
(-8 + z) * x(z + 5) = 0

Reorder the terms:
(-8 + z) * x(5 + z) = 0

Reorder the terms for easier multiplication:
x(-8 + z)(5 + z) = 0

Multiply (-8 + z) * (5 + z)
x(-8(5 + z) + z(5 + z)) = 0
x((5 * -8 + z * -8) + z(5 + z)) = 0
x((-40 + -8z) + z(5 + z)) = 0
x(-40 + -8z + (5 * z + z * z)) = 0
x(-40 + -8z + (5z + z2)) = 0

Combine like terms: -8z + 5z = -3z
x(-40 + -3z + z2) = 0
(-40 * x + -3z * x + z2 * x) = 0
(-40x + -3xz + xz2) = 0

Solving
-40x + -3xz + xz2 = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), 'x'.
x(-40 + -3z + z2) = 0

Factor a trinomial.
x((-5 + -1z)(8 + -1z)) = 0

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 0

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

Add '5' to each side of the equation.
-5 + 5 + -1z = 0 + 5

Combine like terms: -5 + 5 = 0
0 + -1z = 0 + 5
-1z = 0 + 5

Combine like terms: 0 + 5 = 5
-1z = 5

Add 'z' to each side of the equation.
-1z + z = 5 + z

Combine like terms: -1z + z = 0
0 = 5 + z

Simplifying
0 = 5 + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Subproblem 3
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 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 + -1z = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1z = 0 + -8
-1z = 0 + -8

Combine like terms: 0 + -8 = -8
-1z = -8

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

Combine like terms: -1z + z = 0
0 = -8 + z

Simplifying
0 = -8 + z

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}