5n^2-17n+10=4

Solution for 5n^2-17n+10=4 equation:

Simplifying
5n2 + -17n + 10 = 4

Reorder the terms:
10 + -17n + 5n2 = 4

Solving
10 + -17n + 5n2 = 4

Solving for variable 'n'.

Reorder the terms:
10 + -4 + -17n + 5n2 = 4 + -4

Combine like terms: 10 + -4 = 6
6 + -17n + 5n2 = 4 + -4

Combine like terms: 4 + -4 = 0
6 + -17n + 5n2 = 0

Factor a trinomial.
(2 + -5n)(3 + -1n) = 0

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

Simplifying
2 + -5n = 0

Solving
2 + -5n = 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 + -5n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5n = 0 + -2
-5n = 0 + -2

Combine like terms: 0 + -2 = -2
-5n = -2

Divide each side by '-5'.
n = 0.4

Simplifying
n = 0.4
Subproblem 2
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
Solution
n = {0.4, 3}