y^2+14y=-45

Solution for y^2+14y=-45 equation:

Simplifying
y2 + 14y = -45

Reorder the terms:
14y + y2 = -45

Solving
14y + y2 = -45

Solving for variable 'y'.

Reorder the terms:
45 + 14y + y2 = -45 + 45

Combine like terms: -45 + 45 = 0
45 + 14y + y2 = 0

Factor a trinomial.
(9 + y)(5 + y) = 0

Subproblem 1
Set the factor '(9 + y)' equal to zero and attempt to solve:

Simplifying
9 + y = 0

Solving
9 + y = 0

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

Add '-9' to each side of the equation.
9 + -9 + y = 0 + -9

Combine like terms: 9 + -9 = 0
0 + y = 0 + -9
y = 0 + -9

Combine like terms: 0 + -9 = -9
y = -9

Simplifying
y = -9
Subproblem 2
Set the factor '(5 + y)' equal to zero and attempt to solve:

Simplifying
5 + y = 0

Solving
5 + y = 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 + y = 0 + -5

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

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

Simplifying
y = -5
Solution
y = {-9, -5}