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

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

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

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

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

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

Combine like terms: -2z + 5z = 3z
(-10 + 3z + z2) = 0

Solving
-10 + 3z + z2 = 0

Solving for variable 'z'.

Factor a trinomial.
(-5 + -1z)(2 + -1z) = 0

Subproblem 1
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
Subproblem 2
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
Solution
z = {-5, 2}