x^2+26x+52=-53

Solution for x^2+26x+52=-53 equation:

Simplifying
x2 + 26x + 52 = -53

Reorder the terms:
52 + 26x + x2 = -53

Solving
52 + 26x + x2 = -53

Solving for variable 'x'.

Reorder the terms:
52 + 53 + 26x + x2 = -53 + 53

Combine like terms: 52 + 53 = 105
105 + 26x + x2 = -53 + 53

Combine like terms: -53 + 53 = 0
105 + 26x + x2 = 0

Factor a trinomial.
(21 + x)(5 + x) = 0

Subproblem 1
Set the factor '(21 + x)' equal to zero and attempt to solve:

Simplifying
21 + x = 0

Solving
21 + x = 0

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

Add '-21' to each side of the equation.
21 + -21 + x = 0 + -21

Combine like terms: 21 + -21 = 0
0 + x = 0 + -21
x = 0 + -21

Combine like terms: 0 + -21 = -21
x = -21

Simplifying
x = -21
Subproblem 2
Set the factor '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

Solving
5 + x = 0

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

Add '-5' to each side of the equation.
5 + -5 + x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + x = 0 + -5
x = 0 + -5

Combine like terms: 0 + -5 = -5
x = -5

Simplifying
x = -5
Solution
x = {-21, -5}