Simplifying
y^{2} + -10y + 21 = 0
Reorder the terms:
21 + -10y + y^{2} = 0
Solving
21 + -10y + y^{2} = 0
Solving for variable 'y'.
Factor a trinomial.
(3 + -1y)(7 + -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 '(7 + -1y)' equal to zero and attempt to solve:
Simplifying
7 + -1y = 0
Solving
7 + -1y = 0
Move all terms containing y to the left, all other terms to the right.
Add '-7' to each side of the equation.
7 + -7 + -1y = 0 + -7
Combine like terms: 7 + -7 = 0
0 + -1y = 0 + -7
-1y = 0 + -7
Combine like terms: 0 + -7 = -7
-1y = -7
Divide each side by '-1'.
y = 7
Simplifying
y = 7#### Solution

y = {3, 7}