5w^2+w-48=0

Solution for 5w^2+w-48=0 equation:

Simplifying
5w2 + w + -48 = 0

Reorder the terms:
-48 + w + 5w2 = 0

Solving
-48 + w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-16 + -5w)(3 + -1w) = 0

Subproblem 1
Set the factor '(-16 + -5w)' equal to zero and attempt to solve:

Simplifying
-16 + -5w = 0

Solving
-16 + -5w = 0

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

Add '16' to each side of the equation.
-16 + 16 + -5w = 0 + 16

Combine like terms: -16 + 16 = 0
0 + -5w = 0 + 16
-5w = 0 + 16

Combine like terms: 0 + 16 = 16
-5w = 16

Divide each side by '-5'.
w = -3.2

Simplifying
w = -3.2
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 = {-3.2, 3}