(3n-1)(2n-1)=15

Solution for (3n-1)(2n-1)=15 equation:

Simplifying
(3n + -1)(2n + -1) = 15

Reorder the terms:
(-1 + 3n)(2n + -1) = 15

Reorder the terms:
(-1 + 3n)(-1 + 2n) = 15

Multiply (-1 + 3n) * (-1 + 2n)
(-1(-1 + 2n) + 3n * (-1 + 2n)) = 15
((-1 * -1 + 2n * -1) + 3n * (-1 + 2n)) = 15
((1 + -2n) + 3n * (-1 + 2n)) = 15
(1 + -2n + (-1 * 3n + 2n * 3n)) = 15
(1 + -2n + (-3n + 6n2)) = 15

Combine like terms: -2n + -3n = -5n
(1 + -5n + 6n2) = 15

Solving
1 + -5n + 6n2 = 15

Solving for variable 'n'.

Reorder the terms:
1 + -15 + -5n + 6n2 = 15 + -15

Combine like terms: 1 + -15 = -14
-14 + -5n + 6n2 = 15 + -15

Combine like terms: 15 + -15 = 0
-14 + -5n + 6n2 = 0

Factor a trinomial.
(-7 + -6n)(2 + -1n) = 0

Subproblem 1
Set the factor '(-7 + -6n)' equal to zero and attempt to solve:

Simplifying
-7 + -6n = 0

Solving
-7 + -6n = 0

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

Add '7' to each side of the equation.
-7 + 7 + -6n = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -6n = 0 + 7
-6n = 0 + 7

Combine like terms: 0 + 7 = 7
-6n = 7

Divide each side by '-6'.
n = -1.166666667

Simplifying
n = -1.166666667
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 = {-1.166666667, 2}