40w^2-10w-15=0

Solution for 40w^2-10w-15=0 equation:

Simplifying
40w2 + -10w + -15 = 0

Reorder the terms:
-15 + -10w + 40w2 = 0

Solving
-15 + -10w + 40w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '5'.
5(-3 + -2w + 8w2) = 0

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

Ignore the factor 5.
Subproblem 1
Set the factor '(-1 + -2w)' equal to zero and attempt to solve:

Simplifying
-1 + -2w = 0

Solving
-1 + -2w = 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 + -2w = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -2w = 0 + 1
-2w = 0 + 1

Combine like terms: 0 + 1 = 1
-2w = 1

Divide each side by '-2'.
w = -0.5

Simplifying
w = -0.5
Subproblem 2
Set the factor '(3 + -4w)' equal to zero and attempt to solve:

Simplifying
3 + -4w = 0

Solving
3 + -4w = 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 + -4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -4w = 0 + -3
-4w = 0 + -3

Combine like terms: 0 + -3 = -3
-4w = -3

Divide each side by '-4'.
w = 0.75

Simplifying
w = 0.75
Solution
w = {-0.5, 0.75}