(2n-1)(3n+2)=24

Solution for (2n-1)(3n+2)=24 equation:

Simplifying
(2n + -1)(3n + 2) = 24

Reorder the terms:
(-1 + 2n)(3n + 2) = 24

Reorder the terms:
(-1 + 2n)(2 + 3n) = 24

Multiply (-1 + 2n) * (2 + 3n)
(-1(2 + 3n) + 2n * (2 + 3n)) = 24
((2 * -1 + 3n * -1) + 2n * (2 + 3n)) = 24
((-2 + -3n) + 2n * (2 + 3n)) = 24
(-2 + -3n + (2 * 2n + 3n * 2n)) = 24
(-2 + -3n + (4n + 6n2)) = 24

Combine like terms: -3n + 4n = 1n
(-2 + 1n + 6n2) = 24

Solving
-2 + 1n + 6n2 = 24

Solving for variable 'n'.

Reorder the terms:
-2 + -24 + 1n + 6n2 = 24 + -24

Combine like terms: -2 + -24 = -26
-26 + 1n + 6n2 = 24 + -24

Combine like terms: 24 + -24 = 0
-26 + 1n + 6n2 = 0

Factor a trinomial.
(-13 + -6n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-13 + -6n)' equal to zero and attempt to solve:

Simplifying
-13 + -6n = 0

Solving
-13 + -6n = 0

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

Add '13' to each side of the equation.
-13 + 13 + -6n = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -6n = 0 + 13
-6n = 0 + 13

Combine like terms: 0 + 13 = 13
-6n = 13

Divide each side by '-6'.
n = -2.166666667

Simplifying
n = -2.166666667
Subproblem 2
Set the factor '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

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

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

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

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

Simplifying
n = 2
Solution
n = {-2.166666667, 2}