(z-5)(z-2)=0

Solution for (z-5)(z-2)=0 equation:

Simplifying
(z + -5)(z + -2) = 0

Reorder the terms:
(-5 + z)(z + -2) = 0

Reorder the terms:
(-5 + z)(-2 + z) = 0

Multiply (-5 + z) * (-2 + z)
(-5(-2 + z) + z(-2 + z)) = 0
((-2 * -5 + z * -5) + z(-2 + z)) = 0
((10 + -5z) + z(-2 + z)) = 0
(10 + -5z + (-2 * z + z * z)) = 0
(10 + -5z + (-2z + z2)) = 0

Combine like terms: -5z + -2z = -7z
(10 + -7z + z2) = 0

Solving
10 + -7z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(2 + -1z)(5 + -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 '(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 = {2, 5}