2y^2-23y+65=0

Solution for 2y^2-23y+65=0 equation:

Simplifying
2y2 + -23y + 65 = 0

Reorder the terms:
65 + -23y + 2y2 = 0

Solving
65 + -23y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(5 + -1y)(13 + -2y) = 0

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

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

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

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

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

Simplifying
y = 5
Subproblem 2
Set the factor '(13 + -2y)' equal to zero and attempt to solve:

Simplifying
13 + -2y = 0

Solving
13 + -2y = 0

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

Add '-13' to each side of the equation.
13 + -13 + -2y = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -2y = 0 + -13
-2y = 0 + -13

Combine like terms: 0 + -13 = -13
-2y = -13

Divide each side by '-2'.
y = 6.5

Simplifying
y = 6.5
Solution
y = {5, 6.5}