r^2-4r-77=0

Solution for r^2-4r-77=0 equation:

Simplifying
r2 + -4r + -77 = 0

Reorder the terms:
-77 + -4r + r2 = 0

Solving
-77 + -4r + r2 = 0

Solving for variable 'r'.

Factor a trinomial.
(-7 + -1r)(11 + -1r) = 0

Subproblem 1
Set the factor '(-7 + -1r)' equal to zero and attempt to solve:

Simplifying
-7 + -1r = 0

Solving
-7 + -1r = 0

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

Add '7' to each side of the equation.
-7 + 7 + -1r = 0 + 7

Combine like terms: -7 + 7 = 0
0 + -1r = 0 + 7
-1r = 0 + 7

Combine like terms: 0 + 7 = 7
-1r = 7

Divide each side by '-1'.
r = -7

Simplifying
r = -7
Subproblem 2
Set the factor '(11 + -1r)' equal to zero and attempt to solve:

Simplifying
11 + -1r = 0

Solving
11 + -1r = 0

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

Add '-11' to each side of the equation.
11 + -11 + -1r = 0 + -11

Combine like terms: 11 + -11 = 0
0 + -1r = 0 + -11
-1r = 0 + -11

Combine like terms: 0 + -11 = -11
-1r = -11

Divide each side by '-1'.
r = 11

Simplifying
r = 11
Solution
r = {-7, 11}