40w^2-14w-6=0

Solution for 40w^2-14w-6=0 equation:

Simplifying
40w2 + -14w + -6 = 0

Reorder the terms:
-6 + -14w + 40w2 = 0

Solving
-6 + -14w + 40w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -7w + 20w2) = 0

Factor a trinomial.
2((-1 + -4w)(3 + -5w)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -4w)' equal to zero and attempt to solve:

Simplifying
-1 + -4w = 0

Solving
-1 + -4w = 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 + -4w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -4w = 0 + 1
-4w = 0 + 1

Combine like terms: 0 + 1 = 1
-4w = 1

Divide each side by '-4'.
w = -0.25

Simplifying
w = -0.25
Subproblem 2
Set the factor '(3 + -5w)' equal to zero and attempt to solve:

Simplifying
3 + -5w = 0

Solving
3 + -5w = 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 + -5w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5w = 0 + -3
-5w = 0 + -3

Combine like terms: 0 + -3 = -3
-5w = -3

Divide each side by '-5'.
w = 0.6

Simplifying
w = 0.6
Solution
w = {-0.25, 0.6}