6n^2=42+36n

Solution for 6n^2=42+36n equation:

Simplifying
6n2 = 42 + 36n

Solving
6n2 = 42 + 36n

Solving for variable 'n'.

Reorder the terms:
-42 + -36n + 6n2 = 42 + 36n + -42 + -36n

Reorder the terms:
-42 + -36n + 6n2 = 42 + -42 + 36n + -36n

Combine like terms: 42 + -42 = 0
-42 + -36n + 6n2 = 0 + 36n + -36n
-42 + -36n + 6n2 = 36n + -36n

Combine like terms: 36n + -36n = 0
-42 + -36n + 6n2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-7 + -6n + n2) = 0

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

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + -1n)' equal to zero and attempt to solve:

Simplifying
-1 + -1n = 0

Solving
-1 + -1n = 0

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

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

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

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

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

Simplifying
n = -1
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 = {-1, 7}