y^2+24y+52=-67

Solution for y^2+24y+52=-67 equation:

Simplifying
y2 + 24y + 52 = -67

Reorder the terms:
52 + 24y + y2 = -67

Solving
52 + 24y + y2 = -67

Solving for variable 'y'.

Reorder the terms:
52 + 67 + 24y + y2 = -67 + 67

Combine like terms: 52 + 67 = 119
119 + 24y + y2 = -67 + 67

Combine like terms: -67 + 67 = 0
119 + 24y + y2 = 0

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

Subproblem 1
Set the factor '(17 + y)' equal to zero and attempt to solve:

Simplifying
17 + y = 0

Solving
17 + y = 0

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

Add '-17' to each side of the equation.
17 + -17 + y = 0 + -17

Combine like terms: 17 + -17 = 0
0 + y = 0 + -17
y = 0 + -17

Combine like terms: 0 + -17 = -17
y = -17

Simplifying
y = -17
Subproblem 2
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
Solution
y = {-17, -7}