k^2-20k-52=-8

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Solution for k^2-20k-52=-8 equation: 


Simplifying
k2 + -20k + -52 = -8

Reorder the terms:
-52 + -20k + k2 = -8

Solving
-52 + -20k + k2 = -8

Solving for variable 'k'.

Reorder the terms:
-52 + 8 + -20k + k2 = -8 + 8

Combine like terms: -52 + 8 = -44
-44 + -20k + k2 = -8 + 8

Combine like terms: -8 + 8 = 0
-44 + -20k + k2 = 0

Factor a trinomial.
(-2 + -1k)(22 + -1k) = 0


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

Simplifying
-2 + -1k = 0

Solving
-2 + -1k = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1k = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1k = 0 + 2
-1k = 0 + 2

Combine like terms: 0 + 2 = 2
-1k = 2

Divide each side by '-1'.
k = -2

Simplifying
k = -2

Subproblem 2
Set the factor '(22 + -1k)' equal to zero and attempt to solve:

Simplifying
22 + -1k = 0

Solving
22 + -1k = 0

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

Add '-22' to each side of the equation.
22 + -22 + -1k = 0 + -22

Combine like terms: 22 + -22 = 0
0 + -1k = 0 + -22
-1k = 0 + -22

Combine like terms: 0 + -22 = -22
-1k = -22

Divide each side by '-1'.
k = 22

Simplifying
k = 22
Solution
k = {-2, 22}

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