-k^2+2k+6=7

Solution for -k^2+2k+6=7 equation:

Simplifying
-1k2 + 2k + 6 = 7

Reorder the terms:
6 + 2k + -1k2 = 7

Solving
6 + 2k + -1k2 = 7

Solving for variable 'k'.

Reorder the terms:
6 + -7 + 2k + -1k2 = 7 + -7

Combine like terms: 6 + -7 = -1
-1 + 2k + -1k2 = 7 + -7

Combine like terms: 7 + -7 = 0
-1 + 2k + -1k2 = 0

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

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

Simplifying
-1 + k = 0

Solving
-1 + k = 0

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

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

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

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

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

Simplifying
1 + -1k = 0

Solving
1 + -1k = 0

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

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

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

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

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

Simplifying
k = 1
Solution
k = {1, 1}