[5w+1]=[3-w]

Solution for [5w+1]=[3-w] equation:

Simplifying
[5w + 1] = [3 + -1w]

Reorder the terms:
[1 + 5w] = [3 + -1w]

Remove brackets around [1 + 5w]
1 + 5w = [3 + -1w]

Remove brackets around [3 + -1w]
1 + 5w = 3 + -1w

Solving
1 + 5w = 3 + -1w

Solving for variable 'w'.

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

Add 'w' to each side of the equation.
1 + 5w + w = 3 + -1w + w

Combine like terms: 5w + w = 6w
1 + 6w = 3 + -1w + w

Combine like terms: -1w + w = 0
1 + 6w = 3 + 0
1 + 6w = 3

Add '-1' to each side of the equation.
1 + -1 + 6w = 3 + -1

Combine like terms: 1 + -1 = 0
0 + 6w = 3 + -1
6w = 3 + -1

Combine like terms: 3 + -1 = 2
6w = 2

Divide each side by '6'.
w = 0.3333333333

Simplifying
w = 0.3333333333