(q-2)(q-3)=

Solution for (q-2)(q-3)= equation:

Simplifying
(q + -2)(q + -3) = 0

Reorder the terms:
(-2 + q)(q + -3) = 0

Reorder the terms:
(-2 + q)(-3 + q) = 0

Multiply (-2 + q) * (-3 + q)
(-2(-3 + q) + q(-3 + q)) = 0
((-3 * -2 + q * -2) + q(-3 + q)) = 0
((6 + -2q) + q(-3 + q)) = 0
(6 + -2q + (-3 * q + q * q)) = 0
(6 + -2q + (-3q + q2)) = 0

Combine like terms: -2q + -3q = -5q
(6 + -5q + q2) = 0

Solving
6 + -5q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(2 + -1q)(3 + -1q) = 0

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

Simplifying
2 + -1q = 0

Solving
2 + -1q = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1q = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1q = 0 + -2
-1q = 0 + -2

Combine like terms: 0 + -2 = -2
-1q = -2

Divide each side by '-1'.
q = 2

Simplifying
q = 2
Subproblem 2
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
Solution
q = {2, 3}