n*n=42+n

Solution for n*n=42+n equation:

Simplifying
n * n = 42 + n

Multiply n * n
n2 = 42 + n

Solving
n2 = 42 + n

Solving for variable 'n'.

Reorder the terms:
-42 + -1n + n2 = 42 + n + -42 + -1n

Reorder the terms:
-42 + -1n + n2 = 42 + -42 + n + -1n

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

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

Factor a trinomial.
(-6 + -1n)(7 + -1n) = 0

Subproblem 1
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
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 = {-6, 7}