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

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

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

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

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

Multiply (2 + z) * (8 + z)
(2(8 + z) + z(8 + z)) = 0
((8 * 2 + z * 2) + z(8 + z)) = 0
((16 + 2z) + z(8 + z)) = 0
(16 + 2z + (8 * z + z * z)) = 0
(16 + 2z + (8z + z2)) = 0

Combine like terms: 2z + 8z = 10z
(16 + 10z + z2) = 0

Solving
16 + 10z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(8 + z)(2 + z) = 0

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

Simplifying
8 + z = 0

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

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

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

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

Simplifying
2 + z = 0

Solving
2 + z = 0

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

Add '-2' to each side of the equation.
2 + -2 + z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + z = 0 + -2
z = 0 + -2

Combine like terms: 0 + -2 = -2
z = -2

Simplifying
z = -2
Solution
z = {-8, -2}