0=4w^2-23w-6

Solution for 0=4w^2-23w-6 equation:

Simplifying
0 = 4w2 + -23w + -6

Reorder the terms:
0 = -6 + -23w + 4w2

Solving
0 = -6 + -23w + 4w2

Solving for variable 'w'.

Combine like terms: 0 + 6 = 6
6 + 23w + -4w2 = -6 + -23w + 4w2 + 6 + 23w + -4w2

Reorder the terms:
6 + 23w + -4w2 = -6 + 6 + -23w + 23w + 4w2 + -4w2

Combine like terms: -6 + 6 = 0
6 + 23w + -4w2 = 0 + -23w + 23w + 4w2 + -4w2
6 + 23w + -4w2 = -23w + 23w + 4w2 + -4w2

Combine like terms: -23w + 23w = 0
6 + 23w + -4w2 = 0 + 4w2 + -4w2
6 + 23w + -4w2 = 4w2 + -4w2

Combine like terms: 4w2 + -4w2 = 0
6 + 23w + -4w2 = 0

Factor a trinomial.
(6 + -1w)(1 + 4w) = 0

Subproblem 1
Set the factor '(6 + -1w)' equal to zero and attempt to solve:

Simplifying
6 + -1w = 0

Solving
6 + -1w = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1w = 0 + -6
-1w = 0 + -6

Combine like terms: 0 + -6 = -6
-1w = -6

Divide each side by '-1'.
w = 6

Simplifying
w = 6
Subproblem 2
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
Solution
w = {6, -0.25}