x^2-(2k+6)x-(k+1)=0

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Solution for x^2-(2k+6)x-(k+1)=0 equation: 


Simplifying
x2 + -1(2k + 6) * x + -1(k + 1) = 0

Reorder the terms:
x2 + -1(6 + 2k) * x + -1(k + 1) = 0

Reorder the terms for easier multiplication:
x2 + -1x(6 + 2k) + -1(k + 1) = 0
x2 + (6 * -1x + 2k * -1x) + -1(k + 1) = 0

Reorder the terms:
x2 + (-2kx + -6x) + -1(k + 1) = 0
x2 + (-2kx + -6x) + -1(k + 1) = 0

Reorder the terms:
x2 + -2kx + -6x + -1(1 + k) = 0
x2 + -2kx + -6x + (1 * -1 + k * -1) = 0
x2 + -2kx + -6x + (-1 + -1k) = 0

Reorder the terms:
-1 + -1k + -2kx + -6x + x2 = 0

Solving
-1 + -1k + -2kx + -6x + x2 = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + -1k + -2kx + -6x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -1k + -2kx + -6x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -1k + -2kx + -6x + x2 = 0 + 1
-1k + -2kx + -6x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
-1k + -2kx + -6x + x2 = 1

Add '6x' to each side of the equation.
-1k + -2kx + -6x + 6x + x2 = 1 + 6x

Combine like terms: -6x + 6x = 0
-1k + -2kx + 0 + x2 = 1 + 6x
-1k + -2kx + x2 = 1 + 6x

Add '-1x2' to each side of the equation.
-1k + -2kx + x2 + -1x2 = 1 + 6x + -1x2

Combine like terms: x2 + -1x2 = 0
-1k + -2kx + 0 = 1 + 6x + -1x2
-1k + -2kx = 1 + 6x + -1x2

Reorder the terms:
-1 + -1k + -2kx + -6x + x2 = 1 + 6x + -1x2 + -1 + -6x + x2

Reorder the terms:
-1 + -1k + -2kx + -6x + x2 = 1 + -1 + 6x + -6x + -1x2 + x2

Combine like terms: 1 + -1 = 0
-1 + -1k + -2kx + -6x + x2 = 0 + 6x + -6x + -1x2 + x2
-1 + -1k + -2kx + -6x + x2 = 6x + -6x + -1x2 + x2

Combine like terms: 6x + -6x = 0
-1 + -1k + -2kx + -6x + x2 = 0 + -1x2 + x2
-1 + -1k + -2kx + -6x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-1 + -1k + -2kx + -6x + x2 = 0

The solution to this equation could not be determined.

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