(q-3)(q-5)=

Solution for (q-3)(q-5)= equation:

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

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

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

Multiply (-3 + q) * (-5 + q)
(-3(-5 + q) + q(-5 + q)) = 0
((-5 * -3 + q * -3) + q(-5 + q)) = 0
((15 + -3q) + q(-5 + q)) = 0
(15 + -3q + (-5 * q + q * q)) = 0
(15 + -3q + (-5q + q2)) = 0

Combine like terms: -3q + -5q = -8q
(15 + -8q + q2) = 0

Solving
15 + -8q + q2 = 0

Solving for variable 'q'.

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

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

Simplifying
3 + -1q = 0

Solving
3 + -1q = 0

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

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

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

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

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

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

Simplifying
5 + -1q = 0

Solving
5 + -1q = 0

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

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

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

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

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

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