y^2+12y+21=10

Solution for y^2+12y+21=10 equation:

Simplifying
y2 + 12y + 21 = 10

Reorder the terms:
21 + 12y + y2 = 10

Solving
21 + 12y + y2 = 10

Solving for variable 'y'.

Reorder the terms:
21 + -10 + 12y + y2 = 10 + -10

Combine like terms: 21 + -10 = 11
11 + 12y + y2 = 10 + -10

Combine like terms: 10 + -10 = 0
11 + 12y + y2 = 0

Factor a trinomial.
(11 + y)(1 + y) = 0

Subproblem 1
Set the factor '(11 + y)' equal to zero and attempt to solve:

Simplifying
11 + y = 0

Solving
11 + y = 0

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

Add '-11' to each side of the equation.
11 + -11 + y = 0 + -11

Combine like terms: 11 + -11 = 0
0 + y = 0 + -11
y = 0 + -11

Combine like terms: 0 + -11 = -11
y = -11

Simplifying
y = -11
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 = {-11, -1}