7n^2+46n+49=1+6n-n^2

Solution for 7n^2+46n+49=1+6n-n^2 equation:

Simplifying
7n2 + 46n + 49 = 1 + 6n + -1n2

Reorder the terms:
49 + 46n + 7n2 = 1 + 6n + -1n2

Solving
49 + 46n + 7n2 = 1 + 6n + -1n2

Solving for variable 'n'.

Reorder the terms:
49 + -1 + 46n + -6n + 7n2 + n2 = 1 + 6n + -1n2 + -1 + -6n + n2

Combine like terms: 49 + -1 = 48
48 + 46n + -6n + 7n2 + n2 = 1 + 6n + -1n2 + -1 + -6n + n2

Combine like terms: 46n + -6n = 40n
48 + 40n + 7n2 + n2 = 1 + 6n + -1n2 + -1 + -6n + n2

Combine like terms: 7n2 + n2 = 8n2
48 + 40n + 8n2 = 1 + 6n + -1n2 + -1 + -6n + n2

Reorder the terms:
48 + 40n + 8n2 = 1 + -1 + 6n + -6n + -1n2 + n2

Combine like terms: 1 + -1 = 0
48 + 40n + 8n2 = 0 + 6n + -6n + -1n2 + n2
48 + 40n + 8n2 = 6n + -6n + -1n2 + n2

Combine like terms: 6n + -6n = 0
48 + 40n + 8n2 = 0 + -1n2 + n2
48 + 40n + 8n2 = -1n2 + n2

Combine like terms: -1n2 + n2 = 0
48 + 40n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(6 + 5n + n2) = 0

Factor a trinomial.
8((3 + n)(2 + n)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3 + n)' equal to zero and attempt to solve:

Simplifying
3 + n = 0

Solving
3 + n = 0

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

Add '-3' to each side of the equation.
3 + -3 + n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + n = 0 + -3
n = 0 + -3

Combine like terms: 0 + -3 = -3
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(2 + n)' equal to zero and attempt to solve:

Simplifying
2 + n = 0

Solving
2 + n = 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 + n = 0 + -2

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

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

Simplifying
n = -2
Solution
n = {-3, -2}