-7w^2-8w-1=0

Solution for -7w^2-8w-1=0 equation:

Simplifying
-7w2 + -8w + -1 = 0

Reorder the terms:
-1 + -8w + -7w2 = 0

Solving
-1 + -8w + -7w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 8w + 7w2) = 0

Factor a trinomial.
-1((1 + w)(1 + 7w)) = 0

Ignore the factor -1.
Subproblem 1
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 2
Set the factor '(1 + 7w)' equal to zero and attempt to solve:

Simplifying
1 + 7w = 0

Solving
1 + 7w = 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 + 7w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 7w = 0 + -1
7w = 0 + -1

Combine like terms: 0 + -1 = -1
7w = -1

Divide each side by '7'.
w = -0.1428571429

Simplifying
w = -0.1428571429
Solution
w = {-1, -0.1428571429}