y(y+5)=24

Solution for y(y+5)=24 equation:

Simplifying
y(y + 5) = 24

Reorder the terms:
y(5 + y) = 24
(5 * y + y * y) = 24
(5y + y2) = 24

Solving
5y + y2 = 24

Solving for variable 'y'.

Reorder the terms:
-24 + 5y + y2 = 24 + -24

Combine like terms: 24 + -24 = 0
-24 + 5y + y2 = 0

Factor a trinomial.
(-8 + -1y)(3 + -1y) = 0

Subproblem 1
Set the factor '(-8 + -1y)' equal to zero and attempt to solve:

Simplifying
-8 + -1y = 0

Solving
-8 + -1y = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1y = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1y = 0 + 8
-1y = 0 + 8

Combine like terms: 0 + 8 = 8
-1y = 8

Divide each side by '-1'.
y = -8

Simplifying
y = -8
Subproblem 2
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
Solution
y = {-8, 3}