k(k)+8k=84

Solution for k(k)+8k=84 equation:

Simplifying
k(k) + 8k = 84

Multiply k * k
k2 + 8k = 84

Reorder the terms:
8k + k2 = 84

Solving
8k + k2 = 84

Solving for variable 'k'.

Reorder the terms:
-84 + 8k + k2 = 84 + -84

Combine like terms: 84 + -84 = 0
-84 + 8k + k2 = 0

Factor a trinomial.
(-14 + -1k)(6 + -1k) = 0

Subproblem 1
Set the factor '(-14 + -1k)' equal to zero and attempt to solve:

Simplifying
-14 + -1k = 0

Solving
-14 + -1k = 0

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

Add '14' to each side of the equation.
-14 + 14 + -1k = 0 + 14

Combine like terms: -14 + 14 = 0
0 + -1k = 0 + 14
-1k = 0 + 14

Combine like terms: 0 + 14 = 14
-1k = 14

Divide each side by '-1'.
k = -14

Simplifying
k = -14
Subproblem 2
Set the factor '(6 + -1k)' equal to zero and attempt to solve:

Simplifying
6 + -1k = 0

Solving
6 + -1k = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1k = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1k = 0 + -6
-1k = 0 + -6

Combine like terms: 0 + -6 = -6
-1k = -6

Divide each side by '-1'.
k = 6

Simplifying
k = 6
Solution
k = {-14, 6}