2[1-3(w+2)+2(w+3)]=5w

Solution for 2[1-3(w+2)+2(w+3)]=5w equation:

Simplifying
2[1 + -3(w + 2) + 2(w + 3)] = 5w

Reorder the terms:
2[1 + -3(2 + w) + 2(w + 3)] = 5w
2[1 + (2 * -3 + w * -3) + 2(w + 3)] = 5w
2[1 + (-6 + -3w) + 2(w + 3)] = 5w

Reorder the terms:
2[1 + -6 + -3w + 2(3 + w)] = 5w
2[1 + -6 + -3w + (3 * 2 + w * 2)] = 5w
2[1 + -6 + -3w + (6 + 2w)] = 5w

Reorder the terms:
2[1 + -6 + 6 + -3w + 2w] = 5w

Combine like terms: 1 + -6 = -5
2[-5 + 6 + -3w + 2w] = 5w

Combine like terms: -5 + 6 = 1
2[1 + -3w + 2w] = 5w

Combine like terms: -3w + 2w = -1w
2[1 + -1w] = 5w
[1 * 2 + -1w * 2] = 5w
[2 + -2w] = 5w

Solving
2 + -2w = 5w

Solving for variable 'w'.

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

Add '-5w' to each side of the equation.
2 + -2w + -5w = 5w + -5w

Combine like terms: -2w + -5w = -7w
2 + -7w = 5w + -5w

Combine like terms: 5w + -5w = 0
2 + -7w = 0

Add '-2' to each side of the equation.
2 + -2 + -7w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -7w = 0 + -2
-7w = 0 + -2

Combine like terms: 0 + -2 = -2
-7w = -2

Divide each side by '-7'.
w = 0.2857142857

Simplifying
w = 0.2857142857