k^2+14k-53=-2

Solution for k^2+14k-53=-2 equation:

Simplifying
k2 + 14k + -53 = -2

Reorder the terms:
-53 + 14k + k2 = -2

Solving
-53 + 14k + k2 = -2

Solving for variable 'k'.

Reorder the terms:
-53 + 2 + 14k + k2 = -2 + 2

Combine like terms: -53 + 2 = -51
-51 + 14k + k2 = -2 + 2

Combine like terms: -2 + 2 = 0
-51 + 14k + k2 = 0

Factor a trinomial.
(-17 + -1k)(3 + -1k) = 0

Subproblem 1
Set the factor '(-17 + -1k)' equal to zero and attempt to solve:

Simplifying
-17 + -1k = 0

Solving
-17 + -1k = 0

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

Add '17' to each side of the equation.
-17 + 17 + -1k = 0 + 17

Combine like terms: -17 + 17 = 0
0 + -1k = 0 + 17
-1k = 0 + 17

Combine like terms: 0 + 17 = 17
-1k = 17

Divide each side by '-1'.
k = -17

Simplifying
k = -17
Subproblem 2
Set the factor '(3 + -1k)' equal to zero and attempt to solve:

Simplifying
3 + -1k = 0

Solving
3 + -1k = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1k = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1k = 0 + -3
-1k = 0 + -3

Combine like terms: 0 + -3 = -3
-1k = -3

Divide each side by '-1'.
k = 3

Simplifying
k = 3
Solution
k = {-17, 3}