(z+2)*(z-6)=0

Solution for (z+2)*(z-6)=0 equation:

Simplifying
(z + 2)(z + -6) = 0

Reorder the terms:
(2 + z)(z + -6) = 0

Reorder the terms:
(2 + z)(-6 + z) = 0

Multiply (2 + z) * (-6 + z)
(2(-6 + z) + z(-6 + z)) = 0
((-6 * 2 + z * 2) + z(-6 + z)) = 0
((-12 + 2z) + z(-6 + z)) = 0
(-12 + 2z + (-6 * z + z * z)) = 0
(-12 + 2z + (-6z + z2)) = 0

Combine like terms: 2z + -6z = -4z
(-12 + -4z + z2) = 0

Solving
-12 + -4z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-2 + -1z)(6 + -1z) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(6 + -1z)' equal to zero and attempt to solve:

Simplifying
6 + -1z = 0

Solving
6 + -1z = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1z = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1z = 0 + -6
-1z = 0 + -6

Combine like terms: 0 + -6 = -6
-1z = -6

Divide each side by '-1'.
z = 6

Simplifying
z = 6
Solution
z = {-2, 6}