4[2-5(w+3)]+2(w+1)=2[(5w+1)-(w+3)]

Solution for 4[2-5(w+3)]+2(w+1)=2[(5w+1)-(w+3)] equation:

Simplifying
4[2 + -5(w + 3)] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]

Reorder the terms:
4[2 + -5(3 + w)] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]
4[2 + (3 * -5 + w * -5)] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]
4[2 + (-15 + -5w)] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]

Combine like terms: 2 + -15 = -13
4[-13 + -5w] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]
[-13 * 4 + -5w * 4] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]
[-52 + -20w] + 2(w + 1) = 2[(5w + 1) + -1(w + 3)]

Reorder the terms:
-52 + -20w + 2(1 + w) = 2[(5w + 1) + -1(w + 3)]
-52 + -20w + (1 * 2 + w * 2) = 2[(5w + 1) + -1(w + 3)]
-52 + -20w + (2 + 2w) = 2[(5w + 1) + -1(w + 3)]

Reorder the terms:
-52 + 2 + -20w + 2w = 2[(5w + 1) + -1(w + 3)]

Combine like terms: -52 + 2 = -50
-50 + -20w + 2w = 2[(5w + 1) + -1(w + 3)]

Combine like terms: -20w + 2w = -18w
-50 + -18w = 2[(5w + 1) + -1(w + 3)]

Reorder the terms:
-50 + -18w = 2[(1 + 5w) + -1(w + 3)]

Remove parenthesis around (1 + 5w)
-50 + -18w = 2[1 + 5w + -1(w + 3)]

Reorder the terms:
-50 + -18w = 2[1 + 5w + -1(3 + w)]
-50 + -18w = 2[1 + 5w + (3 * -1 + w * -1)]
-50 + -18w = 2[1 + 5w + (-3 + -1w)]

Reorder the terms:
-50 + -18w = 2[1 + -3 + 5w + -1w]

Combine like terms: 1 + -3 = -2
-50 + -18w = 2[-2 + 5w + -1w]

Combine like terms: 5w + -1w = 4w
-50 + -18w = 2[-2 + 4w]
-50 + -18w = [-2 * 2 + 4w * 2]
-50 + -18w = [-4 + 8w]

Solving
-50 + -18w = -4 + 8w

Solving for variable 'w'.

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

Add '-8w' to each side of the equation.
-50 + -18w + -8w = -4 + 8w + -8w

Combine like terms: -18w + -8w = -26w
-50 + -26w = -4 + 8w + -8w

Combine like terms: 8w + -8w = 0
-50 + -26w = -4 + 0
-50 + -26w = -4

Add '50' to each side of the equation.
-50 + 50 + -26w = -4 + 50

Combine like terms: -50 + 50 = 0
0 + -26w = -4 + 50
-26w = -4 + 50

Combine like terms: -4 + 50 = 46
-26w = 46

Divide each side by '-26'.
w = -1.769230769

Simplifying
w = -1.769230769