y^2-52y+420=0

Solution for y^2-52y+420=0 equation:

Simplifying
y2 + -52y + 420 = 0

Reorder the terms:
420 + -52y + y2 = 0

Solving
420 + -52y + y2 = 0

Solving for variable 'y'.

Factor a trinomial.
(10 + -1y)(42 + -1y) = 0

Subproblem 1
Set the factor '(10 + -1y)' equal to zero and attempt to solve:

Simplifying
10 + -1y = 0

Solving
10 + -1y = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1y = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1y = 0 + -10
-1y = 0 + -10

Combine like terms: 0 + -10 = -10
-1y = -10

Divide each side by '-1'.
y = 10

Simplifying
y = 10
Subproblem 2
Set the factor '(42 + -1y)' equal to zero and attempt to solve:

Simplifying
42 + -1y = 0

Solving
42 + -1y = 0

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

Add '-42' to each side of the equation.
42 + -42 + -1y = 0 + -42

Combine like terms: 42 + -42 = 0
0 + -1y = 0 + -42
-1y = 0 + -42

Combine like terms: 0 + -42 = -42
-1y = -42

Divide each side by '-1'.
y = 42

Simplifying
y = 42
Solution
y = {10, 42}