n^2-12n-42=3

Solution for n^2-12n-42=3 equation:

Simplifying
n2 + -12n + -42 = 3

Reorder the terms:
-42 + -12n + n2 = 3

Solving
-42 + -12n + n2 = 3

Solving for variable 'n'.

Reorder the terms:
-42 + -3 + -12n + n2 = 3 + -3

Combine like terms: -42 + -3 = -45
-45 + -12n + n2 = 3 + -3

Combine like terms: 3 + -3 = 0
-45 + -12n + n2 = 0

Factor a trinomial.
(-3 + -1n)(15 + -1n) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(15 + -1n)' equal to zero and attempt to solve:

Simplifying
15 + -1n = 0

Solving
15 + -1n = 0

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

Add '-15' to each side of the equation.
15 + -15 + -1n = 0 + -15

Combine like terms: 15 + -15 = 0
0 + -1n = 0 + -15
-1n = 0 + -15

Combine like terms: 0 + -15 = -15
-1n = -15

Divide each side by '-1'.
n = 15

Simplifying
n = 15
Solution
n = {-3, 15}