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

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

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

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

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

Solving
-2 + y + y2 = 3 + 5y

Solving for variable 'y'.

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

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

Combine like terms: y + -5y = -4y
-5 + -4y + y2 = 3 + 5y + -3 + -5y

Reorder the terms:
-5 + -4y + y2 = 3 + -3 + 5y + -5y

Combine like terms: 3 + -3 = 0
-5 + -4y + y2 = 0 + 5y + -5y
-5 + -4y + y2 = 5y + -5y

Combine like terms: 5y + -5y = 0
-5 + -4y + y2 = 0

Factor a trinomial.
(-1 + -1y)(5 + -1y) = 0

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

Simplifying
-1 + -1y = 0

Solving
-1 + -1y = 0

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

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

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

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

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

Simplifying
y = -1
Subproblem 2
Set the factor '(5 + -1y)' equal to zero and attempt to solve:

Simplifying
5 + -1y = 0

Solving
5 + -1y = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1y = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1y = 0 + -5
-1y = 0 + -5

Combine like terms: 0 + -5 = -5
-1y = -5

Divide each side by '-1'.
y = 5

Simplifying
y = 5
Solution
y = {-1, 5}