2y^2-11y+9=0

Solution for 2y^2-11y+9=0 equation:

Simplifying
2y2 + -11y + 9 = 0

Reorder the terms:
9 + -11y + 2y2 = 0

Solving
9 + -11y + 2y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(1 + -1y)(9 + -2y) = 0

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

Simplifying
1 + -1y = 0

Solving
1 + -1y = 0

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

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

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

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

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

Simplifying
y = 1
Subproblem 2
Set the factor '(9 + -2y)' equal to zero and attempt to solve:

Simplifying
9 + -2y = 0

Solving
9 + -2y = 0

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

Add '-9' to each side of the equation.
9 + -9 + -2y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + -2y = 0 + -9
-2y = 0 + -9

Combine like terms: 0 + -9 = -9
-2y = -9

Divide each side by '-2'.
y = 4.5

Simplifying
y = 4.5
Solution
y = {1, 4.5}