35n^2+6=31n

Solution for 35n^2+6=31n equation:

Simplifying
35n2 + 6 = 31n

Reorder the terms:
6 + 35n2 = 31n

Solving
6 + 35n2 = 31n

Solving for variable 'n'.

Reorder the terms:
6 + -31n + 35n2 = 31n + -31n

Combine like terms: 31n + -31n = 0
6 + -31n + 35n2 = 0

Factor a trinomial.
(2 + -7n)(3 + -5n) = 0

Subproblem 1
Set the factor '(2 + -7n)' equal to zero and attempt to solve:

Simplifying
2 + -7n = 0

Solving
2 + -7n = 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 + -7n = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7n = 0 + -2
-7n = 0 + -2

Combine like terms: 0 + -2 = -2
-7n = -2

Divide each side by '-7'.
n = 0.2857142857

Simplifying
n = 0.2857142857
Subproblem 2
Set the factor '(3 + -5n)' equal to zero and attempt to solve:

Simplifying
3 + -5n = 0

Solving
3 + -5n = 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 + -5n = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5n = 0 + -3
-5n = 0 + -3

Combine like terms: 0 + -3 = -3
-5n = -3

Divide each side by '-5'.
n = 0.6

Simplifying
n = 0.6
Solution
n = {0.2857142857, 0.6}