(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 = 1q
(-6 + 1q + q2) = 0

Solving
-6 + 1q + q2 = 0

Solving for variable 'q'.

Factor a trinomial.
(-3 + -1q)(2 + -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 '(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
Solution
q = {-3, 2}