k^2-2k-77=3

Solution for k^2-2k-77=3 equation:

Simplifying
k2 + -2k + -77 = 3

Reorder the terms:
-77 + -2k + k2 = 3

Solving
-77 + -2k + k2 = 3

Solving for variable 'k'.

Reorder the terms:
-77 + -3 + -2k + k2 = 3 + -3

Combine like terms: -77 + -3 = -80
-80 + -2k + k2 = 3 + -3

Combine like terms: 3 + -3 = 0
-80 + -2k + k2 = 0

Factor a trinomial.
(-8 + -1k)(10 + -1k) = 0

Subproblem 1
Set the factor '(-8 + -1k)' equal to zero and attempt to solve:

Simplifying
-8 + -1k = 0

Solving
-8 + -1k = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1k = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1k = 0 + 8
-1k = 0 + 8

Combine like terms: 0 + 8 = 8
-1k = 8

Divide each side by '-1'.
k = -8

Simplifying
k = -8
Subproblem 2
Set the factor '(10 + -1k)' equal to zero and attempt to solve:

Simplifying
10 + -1k = 0

Solving
10 + -1k = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1k = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1k = 0 + -10
-1k = 0 + -10

Combine like terms: 0 + -10 = -10
-1k = -10

Divide each side by '-1'.
k = 10

Simplifying
k = 10
Solution
k = {-8, 10}