(q+2)(q-1)=28

Solution for (q+2)(q-1)=28 equation:

Simplifying
(q + 2)(q + -1) = 28

Reorder the terms:
(2 + q)(q + -1) = 28

Reorder the terms:
(2 + q)(-1 + q) = 28

Multiply (2 + q) * (-1 + q)
(2(-1 + q) + q(-1 + q)) = 28
((-1 * 2 + q * 2) + q(-1 + q)) = 28
((-2 + 2q) + q(-1 + q)) = 28
(-2 + 2q + (-1 * q + q * q)) = 28
(-2 + 2q + (-1q + q2)) = 28

Combine like terms: 2q + -1q = 1q
(-2 + 1q + q2) = 28

Solving
-2 + 1q + q2 = 28

Solving for variable 'q'.

Reorder the terms:
-2 + -28 + 1q + q2 = 28 + -28

Combine like terms: -2 + -28 = -30
-30 + 1q + q2 = 28 + -28

Combine like terms: 28 + -28 = 0
-30 + 1q + q2 = 0

Factor a trinomial.
(-6 + -1q)(5 + -1q) = 0

Subproblem 1
Set the factor '(-6 + -1q)' equal to zero and attempt to solve:

Simplifying
-6 + -1q = 0

Solving
-6 + -1q = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1q = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1q = 0 + 6
-1q = 0 + 6

Combine like terms: 0 + 6 = 6
-1q = 6

Divide each side by '-1'.
q = -6

Simplifying
q = -6
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 = {-6, 5}