8n^2-42n+13=3

Solution for 8n^2-42n+13=3 equation:

Simplifying
8n2 + -42n + 13 = 3

Reorder the terms:
13 + -42n + 8n2 = 3

Solving
13 + -42n + 8n2 = 3

Solving for variable 'n'.

Reorder the terms:
13 + -3 + -42n + 8n2 = 3 + -3

Combine like terms: 13 + -3 = 10
10 + -42n + 8n2 = 3 + -3

Combine like terms: 3 + -3 = 0
10 + -42n + 8n2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(5 + -21n + 4n2) = 0

Factor a trinomial.
2((1 + -4n)(5 + -1n)) = 0

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

Simplifying
1 + -4n = 0

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

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

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

Divide each side by '-4'.
n = 0.25

Simplifying
n = 0.25
Subproblem 2
Set the factor '(5 + -1n)' equal to zero and attempt to solve:

Simplifying
5 + -1n = 0

Solving
5 + -1n = 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 + -1n = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1n = 0 + -5
-1n = 0 + -5

Combine like terms: 0 + -5 = -5
-1n = -5

Divide each side by '-1'.
n = 5

Simplifying
n = 5
Solution
n = {0.25, 5}