2(y-24)=-y^2

Solution for 2(y-24)=-y^2 equation:

Simplifying
2(y + -24) = -1y2

Reorder the terms:
2(-24 + y) = -1y2
(-24 * 2 + y * 2) = -1y2
(-48 + 2y) = -1y2

Solving
-48 + 2y = -1y2

Solving for variable 'y'.

Combine like terms: -1y2 + y2 = 0
-48 + 2y + y2 = 0

Factor a trinomial.
(-8 + -1y)(6 + -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 '(6 + -1y)' equal to zero and attempt to solve:

Simplifying
6 + -1y = 0

Solving
6 + -1y = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1y = 0 + -6
-1y = 0 + -6

Combine like terms: 0 + -6 = -6
-1y = -6

Divide each side by '-1'.
y = 6

Simplifying
y = 6
Solution
y = {-8, 6}