n^2+12n+42=7

Solution for n^2+12n+42=7 equation:

Simplifying
n2 + 12n + 42 = 7

Reorder the terms:
42 + 12n + n2 = 7

Solving
42 + 12n + n2 = 7

Solving for variable 'n'.

Reorder the terms:
42 + -7 + 12n + n2 = 7 + -7

Combine like terms: 42 + -7 = 35
35 + 12n + n2 = 7 + -7

Combine like terms: 7 + -7 = 0
35 + 12n + n2 = 0

Factor a trinomial.
(7 + n)(5 + n) = 0

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

Simplifying
7 + n = 0

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

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

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

Simplifying
n = -7
Subproblem 2
Set the factor '(5 + n)' equal to zero and attempt to solve:

Simplifying
5 + n = 0

Solving
5 + n = 0

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

Add '-5' to each side of the equation.
5 + -5 + n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + n = 0 + -5
n = 0 + -5

Combine like terms: 0 + -5 = -5
n = -5

Simplifying
n = -5
Solution
n = {-7, -5}