y(y+14)=-33

Solution for y(y+14)=-33 equation:

Simplifying
y(y + 14) = -33

Reorder the terms:
y(14 + y) = -33
(14 * y + y * y) = -33
(14y + y2) = -33

Solving
14y + y2 = -33

Solving for variable 'y'.

Reorder the terms:
33 + 14y + y2 = -33 + 33

Combine like terms: -33 + 33 = 0
33 + 14y + y2 = 0

Factor a trinomial.
(11 + y)(3 + 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 '(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 = {-11, -3}