4w^2-3w-126=0

Solution for 4w^2-3w-126=0 equation:

Simplifying
4w2 + -3w + -126 = 0

Reorder the terms:
-126 + -3w + 4w2 = 0

Solving
-126 + -3w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-21 + -4w)(6 + -1w) = 0

Subproblem 1
Set the factor '(-21 + -4w)' equal to zero and attempt to solve:

Simplifying
-21 + -4w = 0

Solving
-21 + -4w = 0

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

Add '21' to each side of the equation.
-21 + 21 + -4w = 0 + 21

Combine like terms: -21 + 21 = 0
0 + -4w = 0 + 21
-4w = 0 + 21

Combine like terms: 0 + 21 = 21
-4w = 21

Divide each side by '-4'.
w = -5.25

Simplifying
w = -5.25
Subproblem 2
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
Solution
w = {-5.25, 6}