(z-2)(z-6)=

Solution for (z-2)(z-6)= 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 = -8z
(12 + -8z + z2) = 0

Solving
12 + -8z + 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}