y^2+5y-23=3y+1

Solution for y^2+5y-23=3y+1 equation:

Simplifying
y2 + 5y + -23 = 3y + 1

Reorder the terms:
-23 + 5y + y2 = 3y + 1

Reorder the terms:
-23 + 5y + y2 = 1 + 3y

Solving
-23 + 5y + y2 = 1 + 3y

Solving for variable 'y'.

Reorder the terms:
-23 + -1 + 5y + -3y + y2 = 1 + 3y + -1 + -3y

Combine like terms: -23 + -1 = -24
-24 + 5y + -3y + y2 = 1 + 3y + -1 + -3y

Combine like terms: 5y + -3y = 2y
-24 + 2y + y2 = 1 + 3y + -1 + -3y

Reorder the terms:
-24 + 2y + y2 = 1 + -1 + 3y + -3y

Combine like terms: 1 + -1 = 0
-24 + 2y + y2 = 0 + 3y + -3y
-24 + 2y + y2 = 3y + -3y

Combine like terms: 3y + -3y = 0
-24 + 2y + y2 = 0

Factor a trinomial.
(-6 + -1y)(4 + -1y) = 0

Subproblem 1
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
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 = {-6, 4}