y^2+10y=-9

Solution for y^2+10y=-9 equation:

Simplifying
y2 + 10y = -9

Reorder the terms:
10y + y2 = -9

Solving
10y + y2 = -9

Solving for variable 'y'.

Reorder the terms:
9 + 10y + y2 = -9 + 9

Combine like terms: -9 + 9 = 0
9 + 10y + y2 = 0

Factor a trinomial.
(9 + y)(1 + 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 '(1 + y)' equal to zero and attempt to solve:

Simplifying
1 + y = 0

Solving
1 + y = 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 + y = 0 + -1

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

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

Simplifying
y = -1
Solution
y = {-9, -1}