0=y^2+2y+21

Solution for 0=y^2+2y+21 equation:

Simplifying
0 = y2 + 2y + 21

Reorder the terms:
0 = 21 + 2y + y2

Solving
0 = 21 + 2y + y2

Solving for variable 'y'.

Combine like terms: 0 + -21 = -21
-21 + -2y + -1y2 = 21 + 2y + y2 + -21 + -2y + -1y2

Reorder the terms:
-21 + -2y + -1y2 = 21 + -21 + 2y + -2y + y2 + -1y2

Combine like terms: 21 + -21 = 0
-21 + -2y + -1y2 = 0 + 2y + -2y + y2 + -1y2
-21 + -2y + -1y2 = 2y + -2y + y2 + -1y2

Combine like terms: 2y + -2y = 0
-21 + -2y + -1y2 = 0 + y2 + -1y2
-21 + -2y + -1y2 = y2 + -1y2

Combine like terms: y2 + -1y2 = 0
-21 + -2y + -1y2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(21 + 2y + y2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(21 + 2y + y2)' equal to zero and attempt to solve:

Simplifying
21 + 2y + y2 = 0

Solving
21 + 2y + y2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-21' to each side of the equation.
21 + 2y + -21 + y2 = 0 + -21

Reorder the terms:
21 + -21 + 2y + y2 = 0 + -21

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

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

The y term is 2y.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2y + 1 + y2 = -21 + 1

Reorder the terms:
1 + 2y + y2 = -21 + 1

Combine like terms: -21 + 1 = -20
1 + 2y + y2 = -20

Factor a perfect square on the left side:
(y + 1)(y + 1) = -20

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.