3(2n-3)(n-7)=0

Solution for 3(2n-3)(n-7)=0 equation:

Simplifying
3(2n + -3)(n + -7) = 0

Reorder the terms:
3(-3 + 2n)(n + -7) = 0

Reorder the terms:
3(-3 + 2n)(-7 + n) = 0

Multiply (-3 + 2n) * (-7 + n)
3(-3(-7 + n) + 2n * (-7 + n)) = 0
3((-7 * -3 + n * -3) + 2n * (-7 + n)) = 0
3((21 + -3n) + 2n * (-7 + n)) = 0
3(21 + -3n + (-7 * 2n + n * 2n)) = 0
3(21 + -3n + (-14n + 2n2)) = 0

Combine like terms: -3n + -14n = -17n
3(21 + -17n + 2n2) = 0
(21 * 3 + -17n * 3 + 2n2 * 3) = 0
(63 + -51n + 6n2) = 0

Solving
63 + -51n + 6n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '3'.
3(21 + -17n + 2n2) = 0

Factor a trinomial.
3((3 + -2n)(7 + -1n)) = 0

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

Simplifying
3 + -2n = 0

Solving
3 + -2n = 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 + -2n = 0 + -3

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

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

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

Simplifying
n = 1.5
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 = {1.5, 7}