(z+1)(z-8)=0

Solution for (z+1)(z-8)=0 equation:

Simplifying
(z + 1)(z + -8) = 0

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

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

Multiply (1 + z) * (-8 + z)
(1(-8 + z) + z(-8 + z)) = 0
((-8 * 1 + z * 1) + z(-8 + z)) = 0
((-8 + 1z) + z(-8 + z)) = 0
(-8 + 1z + (-8 * z + z * z)) = 0
(-8 + 1z + (-8z + z2)) = 0

Combine like terms: 1z + -8z = -7z
(-8 + -7z + z2) = 0

Solving
-8 + -7z + z2 = 0

Solving for variable 'z'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(8 + -1z)' equal to zero and attempt to solve:

Simplifying
8 + -1z = 0

Solving
8 + -1z = 0

Move all terms containing z 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

Divide each side by '-1'.
z = 8

Simplifying
z = 8
Solution
z = {-1, 8}