(z-1)(z+5)=0

Solution for (z-1)(z+5)=0 equation:

Simplifying
(z + -1)(z + 5) = 0

Reorder the terms:
(-1 + z)(z + 5) = 0

Reorder the terms:
(-1 + z)(5 + z) = 0

Multiply (-1 + z) * (5 + z)
(-1(5 + z) + z(5 + z)) = 0
((5 * -1 + z * -1) + z(5 + z)) = 0
((-5 + -1z) + z(5 + z)) = 0
(-5 + -1z + (5 * z + z * z)) = 0
(-5 + -1z + (5z + z2)) = 0

Combine like terms: -1z + 5z = 4z
(-5 + 4z + z2) = 0

Solving
-5 + 4z + z2 = 0

Solving for variable 'z'.

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

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 '(1 + -1z)' equal to zero and attempt to solve:

Simplifying
1 + -1z = 0

Solving
1 + -1z = 0

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

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

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

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

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

Simplifying
z = 1
Solution
z = {-5, 1}