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

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

Simplifying
n(n + -3) + -7(3 + -1n) = 0

Reorder the terms:
n(-3 + n) + -7(3 + -1n) = 0
(-3 * n + n * n) + -7(3 + -1n) = 0
(-3n + n2) + -7(3 + -1n) = 0
-3n + n2 + (3 * -7 + -1n * -7) = 0
-3n + n2 + (-21 + 7n) = 0

Reorder the terms:
-21 + -3n + 7n + n2 = 0

Combine like terms: -3n + 7n = 4n
-21 + 4n + n2 = 0

Solving
-21 + 4n + n2 = 0

Solving for variable 'n'.

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

Subproblem 1
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
Subproblem 2
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
Solution
n = {-7, 3}