y^2-8y+21=6

Solution for y^2-8y+21=6 equation:

Simplifying
y2 + -8y + 21 = 6

Reorder the terms:
21 + -8y + y2 = 6

Solving
21 + -8y + y2 = 6

Solving for variable 'y'.

Reorder the terms:
21 + -6 + -8y + y2 = 6 + -6

Combine like terms: 21 + -6 = 15
15 + -8y + y2 = 6 + -6

Combine like terms: 6 + -6 = 0
15 + -8y + y2 = 0

Factor a trinomial.
(3 + -1y)(5 + -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 '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {3, 5}