(q+1)(2q-3)=3

Solution for (q+1)(2q-3)=3 equation:

Simplifying
(q + 1)(2q + -3) = 3

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

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

Multiply (1 + q) * (-3 + 2q)
(1(-3 + 2q) + q(-3 + 2q)) = 3
((-3 * 1 + 2q * 1) + q(-3 + 2q)) = 3
((-3 + 2q) + q(-3 + 2q)) = 3
(-3 + 2q + (-3 * q + 2q * q)) = 3
(-3 + 2q + (-3q + 2q2)) = 3

Combine like terms: 2q + -3q = -1q
(-3 + -1q + 2q2) = 3

Solving
-3 + -1q + 2q2 = 3

Solving for variable 'q'.

Reorder the terms:
-3 + -3 + -1q + 2q2 = 3 + -3

Combine like terms: -3 + -3 = -6
-6 + -1q + 2q2 = 3 + -3

Combine like terms: 3 + -3 = 0
-6 + -1q + 2q2 = 0

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

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

Simplifying
-3 + -2q = 0

Solving
-3 + -2q = 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 + -2q = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -2q = 0 + 3
-2q = 0 + 3

Combine like terms: 0 + 3 = 3
-2q = 3

Divide each side by '-2'.
q = -1.5

Simplifying
q = -1.5
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 = {-1.5, 2}