8n^2+60n+35=3+n^2

Solution for 8n^2+60n+35=3+n^2 equation:

Simplifying
8n2 + 60n + 35 = 3 + n2

Reorder the terms:
35 + 60n + 8n2 = 3 + n2

Solving
35 + 60n + 8n2 = 3 + n2

Solving for variable 'n'.

Reorder the terms:
35 + -3 + 60n + 8n2 + -1n2 = 3 + n2 + -3 + -1n2

Combine like terms: 35 + -3 = 32
32 + 60n + 8n2 + -1n2 = 3 + n2 + -3 + -1n2

Combine like terms: 8n2 + -1n2 = 7n2
32 + 60n + 7n2 = 3 + n2 + -3 + -1n2

Reorder the terms:
32 + 60n + 7n2 = 3 + -3 + n2 + -1n2

Combine like terms: 3 + -3 = 0
32 + 60n + 7n2 = 0 + n2 + -1n2
32 + 60n + 7n2 = n2 + -1n2

Combine like terms: n2 + -1n2 = 0
32 + 60n + 7n2 = 0

Factor a trinomial.
(8 + n)(4 + 7n) = 0

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

Simplifying
8 + n = 0

Solving
8 + n = 0

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

Add '-8' to each side of the equation.
8 + -8 + n = 0 + -8

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

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

Simplifying
n = -8
Subproblem 2
Set the factor '(4 + 7n)' equal to zero and attempt to solve:

Simplifying
4 + 7n = 0

Solving
4 + 7n = 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 + 7n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 7n = 0 + -4
7n = 0 + -4

Combine like terms: 0 + -4 = -4
7n = -4

Divide each side by '7'.
n = -0.5714285714

Simplifying
n = -0.5714285714
Solution
n = {-8, -0.5714285714}