6n^2=-42n-36

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

Simplifying
6n2 = -42n + -36

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

Solving
6n2 = -36 + -42n

Solving for variable 'n'.

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

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

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

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

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

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

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

Simplifying
6 + n = 0

Solving
6 + n = 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 + n = 0 + -6

Combine like terms: 6 + -6 = 0
0 + n = 0 + -6
n = 0 + -6

Combine like terms: 0 + -6 = -6
n = -6

Simplifying
n = -6
Subproblem 2
Set the factor '(1 + n)' equal to zero and attempt to solve:

Simplifying
1 + n = 0

Solving
1 + n = 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 + n = 0 + -1

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

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

Simplifying
n = -1
Solution
n = {-6, -1}