(k-3)-(5-3k)=2(k+1)

Solution for (k-3)-(5-3k)=2(k+1) equation:

Simplifying
(k + -3) + -1(5 + -3k) = 2(k + 1)

Reorder the terms:
(-3 + k) + -1(5 + -3k) = 2(k + 1)

Remove parenthesis around (-3 + k)
-3 + k + -1(5 + -3k) = 2(k + 1)
-3 + k + (5 * -1 + -3k * -1) = 2(k + 1)
-3 + k + (-5 + 3k) = 2(k + 1)

Reorder the terms:
-3 + -5 + k + 3k = 2(k + 1)

Combine like terms: -3 + -5 = -8
-8 + k + 3k = 2(k + 1)

Combine like terms: k + 3k = 4k
-8 + 4k = 2(k + 1)

Reorder the terms:
-8 + 4k = 2(1 + k)
-8 + 4k = (1 * 2 + k * 2)
-8 + 4k = (2 + 2k)

Solving
-8 + 4k = 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.
-8 + 4k + -2k = 2 + 2k + -2k

Combine like terms: 4k + -2k = 2k
-8 + 2k = 2 + 2k + -2k

Combine like terms: 2k + -2k = 0
-8 + 2k = 2 + 0
-8 + 2k = 2

Add '8' to each side of the equation.
-8 + 8 + 2k = 2 + 8

Combine like terms: -8 + 8 = 0
0 + 2k = 2 + 8
2k = 2 + 8

Combine like terms: 2 + 8 = 10
2k = 10

Divide each side by '2'.
k = 5

Simplifying
k = 5