y^2+15y+23=6y+5

Solution for y^2+15y+23=6y+5 equation:

Simplifying
y2 + 15y + 23 = 6y + 5

Reorder the terms:
23 + 15y + y2 = 6y + 5

Reorder the terms:
23 + 15y + y2 = 5 + 6y

Solving
23 + 15y + y2 = 5 + 6y

Solving for variable 'y'.

Reorder the terms:
23 + -5 + 15y + -6y + y2 = 5 + 6y + -5 + -6y

Combine like terms: 23 + -5 = 18
18 + 15y + -6y + y2 = 5 + 6y + -5 + -6y

Combine like terms: 15y + -6y = 9y
18 + 9y + y2 = 5 + 6y + -5 + -6y

Reorder the terms:
18 + 9y + y2 = 5 + -5 + 6y + -6y

Combine like terms: 5 + -5 = 0
18 + 9y + y2 = 0 + 6y + -6y
18 + 9y + y2 = 6y + -6y

Combine like terms: 6y + -6y = 0
18 + 9y + y2 = 0

Factor a trinomial.
(6 + y)(3 + y) = 0

Subproblem 1
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 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 + y = 0 + -6

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

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

Simplifying
y = -6
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {-6, -3}