y^2+14y+53=5

Solution for y^2+14y+53=5 equation:

Simplifying
y2 + 14y + 53 = 5

Reorder the terms:
53 + 14y + y2 = 5

Solving
53 + 14y + y2 = 5

Solving for variable 'y'.

Reorder the terms:
53 + -5 + 14y + y2 = 5 + -5

Combine like terms: 53 + -5 = 48
48 + 14y + y2 = 5 + -5

Combine like terms: 5 + -5 = 0
48 + 14y + y2 = 0

Factor a trinomial.
(8 + y)(6 + y) = 0

Subproblem 1
Set the factor '(8 + y)' equal to zero and attempt to solve:

Simplifying
8 + y = 0

Solving
8 + y = 0

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

Add '-8' to each side of the equation.
8 + -8 + y = 0 + -8

Combine like terms: 8 + -8 = 0
0 + y = 0 + -8
y = 0 + -8

Combine like terms: 0 + -8 = -8
y = -8

Simplifying
y = -8
Subproblem 2
Set the factor '(6 + y)' equal to zero and attempt to solve:

Simplifying
6 + y = 0

Solving
6 + y = 0

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

Add '-6' to each side of the equation.
6 + -6 + y = 0 + -6

Combine like terms: 6 + -6 = 0
0 + y = 0 + -6
y = 0 + -6

Combine like terms: 0 + -6 = -6
y = -6

Simplifying
y = -6
Solution
y = {-8, -6}