-2w^2-7w-6=0

Solution for -2w^2-7w-6=0 equation:

Simplifying
-2w2 + -7w + -6 = 0

Reorder the terms:
-6 + -7w + -2w2 = 0

Solving
-6 + -7w + -2w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 7w + 2w2) = 0

Factor a trinomial.
-1((2 + w)(3 + 2w)) = 0

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

Simplifying
2 + w = 0

Solving
2 + w = 0

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

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

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

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

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

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {-2, -1.5}