y^2-14y+33=0

Solution for y^2-14y+33=0 equation:

Simplifying
y2 + -14y + 33 = 0

Reorder the terms:
33 + -14y + y2 = 0

Solving
33 + -14y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(3 + -1y)(11 + -1y) = 0

Subproblem 1
Set the factor '(3 + -1y)' equal to zero and attempt to solve:

Simplifying
3 + -1y = 0

Solving
3 + -1y = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1y = 0 + -3
-1y = 0 + -3

Combine like terms: 0 + -3 = -3
-1y = -3

Divide each side by '-1'.
y = 3

Simplifying
y = 3
Subproblem 2
Set the factor '(11 + -1y)' equal to zero and attempt to solve:

Simplifying
11 + -1y = 0

Solving
11 + -1y = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1y = 0 + -11
-1y = 0 + -11

Combine like terms: 0 + -11 = -11
-1y = -11

Divide each side by '-1'.
y = 11

Simplifying
y = 11
Solution
y = {3, 11}