(z-4)(z-2)=0

Solution for (z-4)(z-2)=0 equation:

Simplifying
(z + -4)(z + -2) = 0

Reorder the terms:
(-4 + z)(z + -2) = 0

Reorder the terms:
(-4 + z)(-2 + z) = 0

Multiply (-4 + z) * (-2 + z)
(-4(-2 + z) + z(-2 + z)) = 0
((-2 * -4 + z * -4) + z(-2 + z)) = 0
((8 + -4z) + z(-2 + z)) = 0
(8 + -4z + (-2 * z + z * z)) = 0
(8 + -4z + (-2z + z2)) = 0

Combine like terms: -4z + -2z = -6z
(8 + -6z + z2) = 0

Solving
8 + -6z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -1z)(4 + -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 '(4 + -1z)' equal to zero and attempt to solve:

Simplifying
4 + -1z = 0

Solving
4 + -1z = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1z = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1z = 0 + -4
-1z = 0 + -4

Combine like terms: 0 + -4 = -4
-1z = -4

Divide each side by '-1'.
z = 4

Simplifying
z = 4
Solution
z = {2, 4}