(z-2)(z+8)=

Solution for (z-2)(z+8)= 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 = 6z
(-16 + 6z + z2) = 0

Solving
-16 + 6z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-8 + -1z)(2 + -1z) = 0

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

Simplifying
2 + -1z = 0

Solving
2 + -1z = 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 + -1z = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1z = 0 + -2
-1z = 0 + -2

Combine like terms: 0 + -2 = -2
-1z = -2

Divide each side by '-1'.
z = 2

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