4w^2-3w-27=0

Solution for 4w^2-3w-27=0 equation:

Simplifying
4w2 + -3w + -27 = 0

Reorder the terms:
-27 + -3w + 4w2 = 0

Solving
-27 + -3w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-9 + -4w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-9 + -4w)' equal to zero and attempt to solve:

Simplifying
-9 + -4w = 0

Solving
-9 + -4w = 0

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

Add '9' to each side of the equation.
-9 + 9 + -4w = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -4w = 0 + 9
-4w = 0 + 9

Combine like terms: 0 + 9 = 9
-4w = 9

Divide each side by '-4'.
w = -2.25

Simplifying
w = -2.25
Subproblem 2
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

Solving
3 + -1w = 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 + -1w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Solution
w = {-2.25, 3}