(z-3)*(z-5)=

Solution for (z-3)*(z-5)= equation:

Simplifying
(z + -3)(z + -5) = 0

Reorder the terms:
(-3 + z)(z + -5) = 0

Reorder the terms:
(-3 + z)(-5 + z) = 0

Multiply (-3 + z) * (-5 + z)
(-3(-5 + z) + z(-5 + z)) = 0
((-5 * -3 + z * -3) + z(-5 + z)) = 0
((15 + -3z) + z(-5 + z)) = 0
(15 + -3z + (-5 * z + z * z)) = 0
(15 + -3z + (-5z + z2)) = 0

Combine like terms: -3z + -5z = -8z
(15 + -8z + z2) = 0

Solving
15 + -8z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(3 + -1z)(5 + -1z) = 0

Subproblem 1
Set the factor '(3 + -1z)' equal to zero and attempt to solve:

Simplifying
3 + -1z = 0

Solving
3 + -1z = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1z = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1z = 0 + -3
-1z = 0 + -3

Combine like terms: 0 + -3 = -3
-1z = -3

Divide each side by '-1'.
z = 3

Simplifying
z = 3
Subproblem 2
Set the factor '(5 + -1z)' equal to zero and attempt to solve:

Simplifying
5 + -1z = 0

Solving
5 + -1z = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1z = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1z = 0 + -5
-1z = 0 + -5

Combine like terms: 0 + -5 = -5
-1z = -5

Divide each side by '-1'.
z = 5

Simplifying
z = 5
Solution
z = {3, 5}