x^2-78x+77=0

Solution for x^2-78x+77=0 equation:

Simplifying
x2 + -78x + 77 = 0

Reorder the terms:
77 + -78x + x2 = 0

Solving
77 + -78x + x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -1x)(77 + -1x) = 0

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

Simplifying
1 + -1x = 0

Solving
1 + -1x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -1x = 0 + -1

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

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

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

Simplifying
x = 1
Subproblem 2
Set the factor '(77 + -1x)' equal to zero and attempt to solve:

Simplifying
77 + -1x = 0

Solving
77 + -1x = 0

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

Add '-77' to each side of the equation.
77 + -77 + -1x = 0 + -77

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

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

Divide each side by '-1'.
x = 77

Simplifying
x = 77
Solution
x = {1, 77}