n[n+1]+3=45

Solution for n[n+1]+3=45 equation:

Simplifying
n[n + 1] + 3 = 45

Reorder the terms:
n[1 + n] + 3 = 45
[1 * n + n * n] + 3 = 45
[1n + n2] + 3 = 45

Reorder the terms:
3 + 1n + n2 = 45

Solving
3 + 1n + n2 = 45

Solving for variable 'n'.

Reorder the terms:
3 + -45 + 1n + n2 = 45 + -45

Combine like terms: 3 + -45 = -42
-42 + 1n + n2 = 45 + -45

Combine like terms: 45 + -45 = 0
-42 + 1n + n2 = 0

Factor a trinomial.
(-7 + -1n)(6 + -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 '(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 = {-7, 6}