0=x^2-77x+1300

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

Simplifying
0 = x2 + -77x + 1300

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

Solving
0 = 1300 + -77x + x2

Solving for variable 'x'.

Combine like terms: 0 + -1300 = -1300
-1300 + 77x + -1x2 = 1300 + -77x + x2 + -1300 + 77x + -1x2

Reorder the terms:
-1300 + 77x + -1x2 = 1300 + -1300 + -77x + 77x + x2 + -1x2

Combine like terms: 1300 + -1300 = 0
-1300 + 77x + -1x2 = 0 + -77x + 77x + x2 + -1x2
-1300 + 77x + -1x2 = -77x + 77x + x2 + -1x2

Combine like terms: -77x + 77x = 0
-1300 + 77x + -1x2 = 0 + x2 + -1x2
-1300 + 77x + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-1300 + 77x + -1x2 = 0

Factor a trinomial.
(-52 + x)(25 + -1x) = 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 + -1x)' equal to zero and attempt to solve:

Simplifying
25 + -1x = 0

Solving
25 + -1x = 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 + -1x = 0 + -25

Combine like terms: 25 + -25 = 0
0 + -1x = 0 + -25
-1x = 0 + -25

Combine like terms: 0 + -25 = -25
-1x = -25

Divide each side by '-1'.
x = 25

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