(2z-8)(z+5)=0

Solution for (2z-8)(z+5)=0 equation:

Simplifying
(2z + -8)(z + 5) = 0

Reorder the terms:
(-8 + 2z)(z + 5) = 0

Reorder the terms:
(-8 + 2z)(5 + z) = 0

Multiply (-8 + 2z) * (5 + z)
(-8(5 + z) + 2z * (5 + z)) = 0
((5 * -8 + z * -8) + 2z * (5 + z)) = 0
((-40 + -8z) + 2z * (5 + z)) = 0
(-40 + -8z + (5 * 2z + z * 2z)) = 0
(-40 + -8z + (10z + 2z2)) = 0

Combine like terms: -8z + 10z = 2z
(-40 + 2z + 2z2) = 0

Solving
-40 + 2z + 2z2 = 0

Solving for variable 'z'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + z + z2) = 0

Factor a trinomial.
2((-5 + -1z)(4 + -1z)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-5 + -1z)' equal to zero and attempt to solve:

Simplifying
-5 + -1z = 0

Solving
-5 + -1z = 0

Move all terms containing z 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

Divide each side by '-1'.
z = -5

Simplifying
z = -5
Subproblem 2
Set the factor '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {-5, 4}