y^2=-10y-21

Solution for y^2=-10y-21 equation:

Simplifying
y2 = -10y + -21

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

Solving
y2 = -21 + -10y

Solving for variable 'y'.

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

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

Combine like terms: -21 + 21 = 0
21 + 10y + y2 = 0 + -10y + 10y
21 + 10y + y2 = -10y + 10y

Combine like terms: -10y + 10y = 0
21 + 10y + y2 = 0

Factor a trinomial.
(7 + y)(3 + y) = 0

Subproblem 1
Set the factor '(7 + y)' equal to zero and attempt to solve:

Simplifying
7 + y = 0

Solving
7 + y = 0

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

Add '-7' to each side of the equation.
7 + -7 + y = 0 + -7

Combine like terms: 7 + -7 = 0
0 + y = 0 + -7
y = 0 + -7

Combine like terms: 0 + -7 = -7
y = -7

Simplifying
y = -7
Subproblem 2
Set the factor '(3 + y)' equal to zero and attempt to solve:

Simplifying
3 + y = 0

Solving
3 + y = 0

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

Add '-3' to each side of the equation.
3 + -3 + y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + y = 0 + -3
y = 0 + -3

Combine like terms: 0 + -3 = -3
y = -3

Simplifying
y = -3
Solution
y = {-7, -3}