3n^2+18n=42+3n

Solution for 3n^2+18n=42+3n equation:

Simplifying
3n2 + 18n = 42 + 3n

Reorder the terms:
18n + 3n2 = 42 + 3n

Solving
18n + 3n2 = 42 + 3n

Solving for variable 'n'.

Reorder the terms:
-42 + 18n + -3n + 3n2 = 42 + 3n + -42 + -3n

Combine like terms: 18n + -3n = 15n
-42 + 15n + 3n2 = 42 + 3n + -42 + -3n

Reorder the terms:
-42 + 15n + 3n2 = 42 + -42 + 3n + -3n

Combine like terms: 42 + -42 = 0
-42 + 15n + 3n2 = 0 + 3n + -3n
-42 + 15n + 3n2 = 3n + -3n

Combine like terms: 3n + -3n = 0
-42 + 15n + 3n2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-14 + 5n + n2) = 0

Factor a trinomial.
3((-7 + -1n)(2 + -1n)) = 0

Ignore the factor 3.
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 '(2 + -1n)' equal to zero and attempt to solve:

Simplifying
2 + -1n = 0

Solving
2 + -1n = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1n = 0 + -2
-1n = 0 + -2

Combine like terms: 0 + -2 = -2
-1n = -2

Divide each side by '-1'.
n = 2

Simplifying
n = 2
Solution
n = {-7, 2}