n^2+33n+6=2-7n^2

Solution for n^2+33n+6=2-7n^2 equation:

Simplifying
n2 + 33n + 6 = 2 + -7n2

Reorder the terms:
6 + 33n + n2 = 2 + -7n2

Solving
6 + 33n + n2 = 2 + -7n2

Solving for variable 'n'.

Reorder the terms:
6 + -2 + 33n + n2 + 7n2 = 2 + -7n2 + -2 + 7n2

Combine like terms: 6 + -2 = 4
4 + 33n + n2 + 7n2 = 2 + -7n2 + -2 + 7n2

Combine like terms: n2 + 7n2 = 8n2
4 + 33n + 8n2 = 2 + -7n2 + -2 + 7n2

Reorder the terms:
4 + 33n + 8n2 = 2 + -2 + -7n2 + 7n2

Combine like terms: 2 + -2 = 0
4 + 33n + 8n2 = 0 + -7n2 + 7n2
4 + 33n + 8n2 = -7n2 + 7n2

Combine like terms: -7n2 + 7n2 = 0
4 + 33n + 8n2 = 0

Factor a trinomial.
(4 + n)(1 + 8n) = 0

Subproblem 1
Set the factor '(4 + n)' equal to zero and attempt to solve:

Simplifying
4 + n = 0

Solving
4 + n = 0

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

Add '-4' to each side of the equation.
4 + -4 + n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + n = 0 + -4
n = 0 + -4

Combine like terms: 0 + -4 = -4
n = -4

Simplifying
n = -4
Subproblem 2
Set the factor '(1 + 8n)' equal to zero and attempt to solve:

Simplifying
1 + 8n = 0

Solving
1 + 8n = 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 + 8n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 8n = 0 + -1
8n = 0 + -1

Combine like terms: 0 + -1 = -1
8n = -1

Divide each side by '8'.
n = -0.125

Simplifying
n = -0.125
Solution
n = {-4, -0.125}