2[k-(2k+19)+18]=2(k+1)

Solution for 2[k-(2k+19)+18]=2(k+1) equation:

Simplifying
2[k + -1(2k + 19) + 18] = 2(k + 1)

Reorder the terms:
2[k + -1(19 + 2k) + 18] = 2(k + 1)
2[k + (19 * -1 + 2k * -1) + 18] = 2(k + 1)
2[k + (-19 + -2k) + 18] = 2(k + 1)

Reorder the terms:
2[-19 + 18 + k + -2k] = 2(k + 1)

Combine like terms: -19 + 18 = -1
2[-1 + k + -2k] = 2(k + 1)

Combine like terms: k + -2k = -1k
2[-1 + -1k] = 2(k + 1)
[-1 * 2 + -1k * 2] = 2(k + 1)
[-2 + -2k] = 2(k + 1)

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

Solving
-2 + -2k = 2 + 2k

Solving for variable 'k'.

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

Add '-2k' to each side of the equation.
-2 + -2k + -2k = 2 + 2k + -2k

Combine like terms: -2k + -2k = -4k
-2 + -4k = 2 + 2k + -2k

Combine like terms: 2k + -2k = 0
-2 + -4k = 2 + 0
-2 + -4k = 2

Add '2' to each side of the equation.
-2 + 2 + -4k = 2 + 2

Combine like terms: -2 + 2 = 0
0 + -4k = 2 + 2
-4k = 2 + 2

Combine like terms: 2 + 2 = 4
-4k = 4

Divide each side by '-4'.
k = -1

Simplifying
k = -1