y^2+23y=2y-90

Solution for y^2+23y=2y-90 equation:

Simplifying
y2 + 23y = 2y + -90

Reorder the terms:
23y + y2 = 2y + -90

Reorder the terms:
23y + y2 = -90 + 2y

Solving
23y + y2 = -90 + 2y

Solving for variable 'y'.

Reorder the terms:
90 + 23y + -2y + y2 = -90 + 2y + 90 + -2y

Combine like terms: 23y + -2y = 21y
90 + 21y + y2 = -90 + 2y + 90 + -2y

Reorder the terms:
90 + 21y + y2 = -90 + 90 + 2y + -2y

Combine like terms: -90 + 90 = 0
90 + 21y + y2 = 0 + 2y + -2y
90 + 21y + y2 = 2y + -2y

Combine like terms: 2y + -2y = 0
90 + 21y + y2 = 0

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

Subproblem 1
Set the factor '(15 + y)' equal to zero and attempt to solve:

Simplifying
15 + y = 0

Solving
15 + y = 0

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

Add '-15' to each side of the equation.
15 + -15 + y = 0 + -15

Combine like terms: 15 + -15 = 0
0 + y = 0 + -15
y = 0 + -15

Combine like terms: 0 + -15 = -15
y = -15

Simplifying
y = -15
Subproblem 2
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
Solution
y = {-15, -6}