2n^2-9n+5=1

Solution for 2n^2-9n+5=1 equation:

Simplifying
2n2 + -9n + 5 = 1

Reorder the terms:
5 + -9n + 2n2 = 1

Solving
5 + -9n + 2n2 = 1

Solving for variable 'n'.

Reorder the terms:
5 + -1 + -9n + 2n2 = 1 + -1

Combine like terms: 5 + -1 = 4
4 + -9n + 2n2 = 1 + -1

Combine like terms: 1 + -1 = 0
4 + -9n + 2n2 = 0

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

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

Simplifying
1 + -2n = 0

Solving
1 + -2n = 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 + -2n = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2n = 0 + -1
-2n = 0 + -1

Combine like terms: 0 + -1 = -1
-2n = -1

Divide each side by '-2'.
n = 0.5

Simplifying
n = 0.5
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 = {0.5, 4}