y^2-40y+204=0

Solution for y^2-40y+204=0 equation:

Simplifying
y2 + -40y + 204 = 0

Reorder the terms:
204 + -40y + y2 = 0

Solving
204 + -40y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(6 + -1y)(34 + -1y) = 0

Subproblem 1
Set the factor '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Subproblem 2
Set the factor '(34 + -1y)' equal to zero and attempt to solve:

Simplifying
34 + -1y = 0

Solving
34 + -1y = 0

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

Add '-34' to each side of the equation.
34 + -34 + -1y = 0 + -34

Combine like terms: 34 + -34 = 0
0 + -1y = 0 + -34
-1y = 0 + -34

Combine like terms: 0 + -34 = -34
-1y = -34

Divide each side by '-1'.
y = 34

Simplifying
y = 34
Solution
y = {6, 34}