8n^2-23n-5=8n-1

Solution for 8n^2-23n-5=8n-1 equation:

Simplifying
8n2 + -23n + -5 = 8n + -1

Reorder the terms:
-5 + -23n + 8n2 = 8n + -1

Reorder the terms:
-5 + -23n + 8n2 = -1 + 8n

Solving
-5 + -23n + 8n2 = -1 + 8n

Solving for variable 'n'.

Reorder the terms:
-5 + 1 + -23n + -8n + 8n2 = -1 + 8n + 1 + -8n

Combine like terms: -5 + 1 = -4
-4 + -23n + -8n + 8n2 = -1 + 8n + 1 + -8n

Combine like terms: -23n + -8n = -31n
-4 + -31n + 8n2 = -1 + 8n + 1 + -8n

Reorder the terms:
-4 + -31n + 8n2 = -1 + 1 + 8n + -8n

Combine like terms: -1 + 1 = 0
-4 + -31n + 8n2 = 0 + 8n + -8n
-4 + -31n + 8n2 = 8n + -8n

Combine like terms: 8n + -8n = 0
-4 + -31n + 8n2 = 0

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

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

Simplifying
4 + -1n = 0

Solving
4 + -1n = 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 + -1n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1n = 0 + -4
-1n = 0 + -4

Combine like terms: 0 + -4 = -4
-1n = -4

Divide each side by '-1'.
n = 4

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