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

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

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

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

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

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

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

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

Solving
6 + -2kx = 0

Solving for variable 'k'.

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

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

Combine like terms: 6 + -6 = 0
0 + -2kx = 0 + -6
-2kx = 0 + -6

Combine like terms: 0 + -6 = -6
-2kx = -6

Divide each side by '-2x'.
k = 3x-1

Simplifying
k = 3x-1