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.
(-6 + -1w)(21 + -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 '(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
Solution
w = {-6, 5.25}