-4(3w-1)8w=2+2(7w-1)

Solution for -4(3w-1)8w=2+2(7w-1) equation:

Simplifying
-4(3w + -1) * 8w = 2 + 2(7w + -1)

Reorder the terms:
-4(-1 + 3w) * 8w = 2 + 2(7w + -1)

Reorder the terms for easier multiplication:
-4 * 8w(-1 + 3w) = 2 + 2(7w + -1)

Multiply -4 * 8
-32w(-1 + 3w) = 2 + 2(7w + -1)
(-1 * -32w + 3w * -32w) = 2 + 2(7w + -1)
(32w + -96w2) = 2 + 2(7w + -1)

Reorder the terms:
32w + -96w2 = 2 + 2(-1 + 7w)
32w + -96w2 = 2 + (-1 * 2 + 7w * 2)
32w + -96w2 = 2 + (-2 + 14w)

Combine like terms: 2 + -2 = 0
32w + -96w2 = 0 + 14w
32w + -96w2 = 14w

Solving
32w + -96w2 = 14w

Solving for variable 'w'.

Reorder the terms:
32w + -14w + -96w2 = 14w + -14w

Combine like terms: 32w + -14w = 18w
18w + -96w2 = 14w + -14w

Combine like terms: 14w + -14w = 0
18w + -96w2 = 0

Factor out the Greatest Common Factor (GCF), '6w'.
6w(3 + -16w) = 0

Ignore the factor 6.
Subproblem 1
Set the factor 'w' equal to zero and attempt to solve:

Simplifying
w = 0

Solving
w = 0

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

Simplifying
w = 0
Subproblem 2
Set the factor '(3 + -16w)' equal to zero and attempt to solve:

Simplifying
3 + -16w = 0

Solving
3 + -16w = 0

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

Add '-3' to each side of the equation.
3 + -3 + -16w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -16w = 0 + -3
-16w = 0 + -3

Combine like terms: 0 + -3 = -3
-16w = -3

Divide each side by '-16'.
w = 0.1875

Simplifying
w = 0.1875
Solution
w = {0, 0.1875}