-7w(-3w^2-1)+(-2w)(8w^2+6)=

Solution for -7w(-3w^2-1)+(-2w)(8w^2+6)= equation:

Simplifying
-7w(-3w2 + -1) + (-2w)(8w2 + 6) = 0

Reorder the terms:
-7w(-1 + -3w2) + (-2w)(8w2 + 6) = 0
(-1 * -7w + -3w2 * -7w) + (-2w)(8w2 + 6) = 0
(7w + 21w3) + (-2w)(8w2 + 6) = 0

Remove parenthesis around (-2w)
7w + 21w3 + -2w(8w2 + 6) = 0

Reorder the terms:
7w + 21w3 + -2w(6 + 8w2) = 0
7w + 21w3 + (6 * -2w + 8w2 * -2w) = 0
7w + 21w3 + (-12w + -16w3) = 0

Reorder the terms:
7w + -12w + 21w3 + -16w3 = 0

Combine like terms: 7w + -12w = -5w
-5w + 21w3 + -16w3 = 0

Combine like terms: 21w3 + -16w3 = 5w3
-5w + 5w3 = 0

Solving
-5w + 5w3 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5w'.
5w(-1 + w2) = 0

Factor a difference between two squares.
5w((1 + w)(-1 + w)) = 0

Ignore the factor 5.
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 '(1 + w)' equal to zero and attempt to solve:

Simplifying
1 + w = 0

Solving
1 + w = 0

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

Add '-1' to each side of the equation.
1 + -1 + w = 0 + -1

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

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

Simplifying
w = -1
Subproblem 3
Set the factor '(-1 + w)' equal to zero and attempt to solve:

Simplifying
-1 + w = 0

Solving
-1 + w = 0

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

Add '1' to each side of the equation.
-1 + 1 + w = 0 + 1

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

Combine like terms: 0 + 1 = 1
w = 1

Simplifying
w = 1
Solution
w = {0, -1, 1}