k^2+2k+6=69

Solution for k^2+2k+6=69 equation:

Simplifying
k2 + 2k + 6 = 69

Reorder the terms:
6 + 2k + k2 = 69

Solving
6 + 2k + k2 = 69

Solving for variable 'k'.

Reorder the terms:
6 + -69 + 2k + k2 = 69 + -69

Combine like terms: 6 + -69 = -63
-63 + 2k + k2 = 69 + -69

Combine like terms: 69 + -69 = 0
-63 + 2k + k2 = 0

Factor a trinomial.
(-9 + -1k)(7 + -1k) = 0

Subproblem 1
Set the factor '(-9 + -1k)' equal to zero and attempt to solve:

Simplifying
-9 + -1k = 0

Solving
-9 + -1k = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1k = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1k = 0 + 9
-1k = 0 + 9

Combine like terms: 0 + 9 = 9
-1k = 9

Divide each side by '-1'.
k = -9

Simplifying
k = -9
Subproblem 2
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
Solution
k = {-9, 7}