(z-5)(z+3)=

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

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

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

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

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

Combine like terms: -5z + 3z = -2z
(-15 + -2z + z2) = 0

Solving
-15 + -2z + 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}