8n^2+25n-14=6n+1

Solution for 8n^2+25n-14=6n+1 equation:

Simplifying
8n2 + 25n + -14 = 6n + 1

Reorder the terms:
-14 + 25n + 8n2 = 6n + 1

Reorder the terms:
-14 + 25n + 8n2 = 1 + 6n

Solving
-14 + 25n + 8n2 = 1 + 6n

Solving for variable 'n'.

Reorder the terms:
-14 + -1 + 25n + -6n + 8n2 = 1 + 6n + -1 + -6n

Combine like terms: -14 + -1 = -15
-15 + 25n + -6n + 8n2 = 1 + 6n + -1 + -6n

Combine like terms: 25n + -6n = 19n
-15 + 19n + 8n2 = 1 + 6n + -1 + -6n

Reorder the terms:
-15 + 19n + 8n2 = 1 + -1 + 6n + -6n

Combine like terms: 1 + -1 = 0
-15 + 19n + 8n2 = 0 + 6n + -6n
-15 + 19n + 8n2 = 6n + -6n

Combine like terms: 6n + -6n = 0
-15 + 19n + 8n2 = 0

Factor a trinomial.
(-3 + -1n)(5 + -8n) = 0

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

Simplifying
-3 + -1n = 0

Solving
-3 + -1n = 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 + -1n = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -1n = 0 + 3
-1n = 0 + 3

Combine like terms: 0 + 3 = 3
-1n = 3

Divide each side by '-1'.
n = -3

Simplifying
n = -3
Subproblem 2
Set the factor '(5 + -8n)' equal to zero and attempt to solve:

Simplifying
5 + -8n = 0

Solving
5 + -8n = 0

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

Add '-5' to each side of the equation.
5 + -5 + -8n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -8n = 0 + -5
-8n = 0 + -5

Combine like terms: 0 + -5 = -5
-8n = -5

Divide each side by '-8'.
n = 0.625

Simplifying
n = 0.625
Solution
n = {-3, 0.625}