23y-y^2=76

Solution for 23y-y^2=76 equation:

Simplifying
23y + -1y2 = 76

Solving
23y + -1y2 = 76

Solving for variable 'y'.

Reorder the terms:
-76 + 23y + -1y2 = 76 + -76

Combine like terms: 76 + -76 = 0
-76 + 23y + -1y2 = 0

Factor a trinomial.
(-19 + y)(4 + -1y) = 0

Subproblem 1
Set the factor '(-19 + y)' equal to zero and attempt to solve:

Simplifying
-19 + y = 0

Solving
-19 + y = 0

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

Add '19' to each side of the equation.
-19 + 19 + y = 0 + 19

Combine like terms: -19 + 19 = 0
0 + y = 0 + 19
y = 0 + 19

Combine like terms: 0 + 19 = 19
y = 19

Simplifying
y = 19
Subproblem 2
Set the factor '(4 + -1y)' equal to zero and attempt to solve:

Simplifying
4 + -1y = 0

Solving
4 + -1y = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1y = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1y = 0 + -4
-1y = 0 + -4

Combine like terms: 0 + -4 = -4
-1y = -4

Divide each side by '-1'.
y = 4

Simplifying
y = 4
Solution
y = {19, 4}