(2n-14)(3n-9)=0

Solution for (2n-14)(3n-9)=0 equation:

Simplifying
(2n + -14)(3n + -9) = 0

Reorder the terms:
(-14 + 2n)(3n + -9) = 0

Reorder the terms:
(-14 + 2n)(-9 + 3n) = 0

Multiply (-14 + 2n) * (-9 + 3n)
(-14(-9 + 3n) + 2n * (-9 + 3n)) = 0
((-9 * -14 + 3n * -14) + 2n * (-9 + 3n)) = 0
((126 + -42n) + 2n * (-9 + 3n)) = 0
(126 + -42n + (-9 * 2n + 3n * 2n)) = 0
(126 + -42n + (-18n + 6n2)) = 0

Combine like terms: -42n + -18n = -60n
(126 + -60n + 6n2) = 0

Solving
126 + -60n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '6'.
6(21 + -10n + n2) = 0

Factor a trinomial.
6((3 + -1n)(7 + -1n)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(3 + -1n)' equal to zero and attempt to solve:

Simplifying
3 + -1n = 0

Solving
3 + -1n = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1n = 0 + -3
-1n = 0 + -3

Combine like terms: 0 + -3 = -3
-1n = -3

Divide each side by '-1'.
n = 3

Simplifying
n = 3
Subproblem 2
Set the factor '(7 + -1n)' equal to zero and attempt to solve:

Simplifying
7 + -1n = 0

Solving
7 + -1n = 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 + -1n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -1n = 0 + -7
-1n = 0 + -7

Combine like terms: 0 + -7 = -7
-1n = -7

Divide each side by '-1'.
n = 7

Simplifying
n = 7
Solution
n = {3, 7}