y^2=24-5y

Solution for y^2=24-5y equation:

Simplifying
y2 = 24 + -5y

Solving
y2 = 24 + -5y

Solving for variable 'y'.

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

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

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

Combine like terms: -5y + 5y = 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}