k^2-5k-84=0

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Solution for k^2-5k-84=0 equation: 


Simplifying
k2 + -5k + -84 = 0

Reorder the terms:
-84 + -5k + k2 = 0

Solving
-84 + -5k + k2 = 0

Solving for variable 'k'.

Factor a trinomial.
(-7 + -1k)(12 + -1k) = 0


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

Simplifying
-7 + -1k = 0

Solving
-7 + -1k = 0

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

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

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

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

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

Simplifying
k = -7

Subproblem 2
Set the factor '(12 + -1k)' equal to zero and attempt to solve:

Simplifying
12 + -1k = 0

Solving
12 + -1k = 0

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

Add '-12' to each side of the equation.
12 + -12 + -1k = 0 + -12

Combine like terms: 12 + -12 = 0
0 + -1k = 0 + -12
-1k = 0 + -12

Combine like terms: 0 + -12 = -12
-1k = -12

Divide each side by '-1'.
k = 12

Simplifying
k = 12
Solution
k = {-7, 12}

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