y(y+8)=65

Solution for y(y+8)=65 equation:

Simplifying
y(y + 8) = 65

Reorder the terms:
y(8 + y) = 65
(8 * y + y * y) = 65
(8y + y2) = 65

Solving
8y + y2 = 65

Solving for variable 'y'.

Reorder the terms:
-65 + 8y + y2 = 65 + -65

Combine like terms: 65 + -65 = 0
-65 + 8y + y2 = 0

Factor a trinomial.
(-13 + -1y)(5 + -1y) = 0

Subproblem 1
Set the factor '(-13 + -1y)' equal to zero and attempt to solve:

Simplifying
-13 + -1y = 0

Solving
-13 + -1y = 0

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

Add '13' to each side of the equation.
-13 + 13 + -1y = 0 + 13

Combine like terms: -13 + 13 = 0
0 + -1y = 0 + 13
-1y = 0 + 13

Combine like terms: 0 + 13 = 13
-1y = 13

Divide each side by '-1'.
y = -13

Simplifying
y = -13
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 = {-13, 5}