(2y+3)=(y^2-5)

Solution for (2y+3)=(y^2-5) equation:

Simplifying
(2y + 3) = (y2 + -5)

Reorder the terms:
(3 + 2y) = (y2 + -5)

Remove parenthesis around (3 + 2y)
3 + 2y = (y2 + -5)

Reorder the terms:
3 + 2y = (-5 + y2)

Remove parenthesis around (-5 + y2)
3 + 2y = -5 + y2

Solving
3 + 2y = -5 + y2

Solving for variable 'y'.

Reorder the terms:
3 + 5 + 2y + -1y2 = -5 + y2 + 5 + -1y2

Combine like terms: 3 + 5 = 8
8 + 2y + -1y2 = -5 + y2 + 5 + -1y2

Reorder the terms:
8 + 2y + -1y2 = -5 + 5 + y2 + -1y2

Combine like terms: -5 + 5 = 0
8 + 2y + -1y2 = 0 + y2 + -1y2
8 + 2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
8 + 2y + -1y2 = 0

Factor a trinomial.
(4 + -1y)(2 + y) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(2 + y)' equal to zero and attempt to solve:

Simplifying
2 + y = 0

Solving
2 + y = 0

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

Add '-2' to each side of the equation.
2 + -2 + y = 0 + -2

Combine like terms: 2 + -2 = 0
0 + y = 0 + -2
y = 0 + -2

Combine like terms: 0 + -2 = -2
y = -2

Simplifying
y = -2
Solution
y = {4, -2}