(n-6)(2n-7)=0

Solution for (n-6)(2n-7)=0 equation:

Simplifying
(n + -6)(2n + -7) = 0

Reorder the terms:
(-6 + n)(2n + -7) = 0

Reorder the terms:
(-6 + n)(-7 + 2n) = 0

Multiply (-6 + n) * (-7 + 2n)
(-6(-7 + 2n) + n(-7 + 2n)) = 0
((-7 * -6 + 2n * -6) + n(-7 + 2n)) = 0
((42 + -12n) + n(-7 + 2n)) = 0
(42 + -12n + (-7 * n + 2n * n)) = 0
(42 + -12n + (-7n + 2n2)) = 0

Combine like terms: -12n + -7n = -19n
(42 + -19n + 2n2) = 0

Solving
42 + -19n + 2n2 = 0

Solving for variable 'n'.

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

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

Simplifying
7 + -2n = 0

Solving
7 + -2n = 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 + -2n = 0 + -7

Combine like terms: 7 + -7 = 0
0 + -2n = 0 + -7
-2n = 0 + -7

Combine like terms: 0 + -7 = -7
-2n = -7

Divide each side by '-2'.
n = 3.5

Simplifying
n = 3.5
Subproblem 2
Set the factor '(6 + -1n)' equal to zero and attempt to solve:

Simplifying
6 + -1n = 0

Solving
6 + -1n = 0

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

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

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

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

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

Simplifying
n = 6
Solution
n = {3.5, 6}