x^2+77x+1300=0

Solution for x^2+77x+1300=0 equation:

Simplifying
x2 + 77x + 1300 = 0

Reorder the terms:
1300 + 77x + x2 = 0

Solving
1300 + 77x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(52 + x)(25 + x) = 0

Subproblem 1
Set the factor '(52 + x)' equal to zero and attempt to solve:

Simplifying
52 + x = 0

Solving
52 + x = 0

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

Add '-52' to each side of the equation.
52 + -52 + x = 0 + -52

Combine like terms: 52 + -52 = 0
0 + x = 0 + -52
x = 0 + -52

Combine like terms: 0 + -52 = -52
x = -52

Simplifying
x = -52
Subproblem 2
Set the factor '(25 + x)' equal to zero and attempt to solve:

Simplifying
25 + x = 0

Solving
25 + x = 0

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

Add '-25' to each side of the equation.
25 + -25 + x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + x = 0 + -25
x = 0 + -25

Combine like terms: 0 + -25 = -25
x = -25

Simplifying
x = -25
Solution
x = {-52, -25}