5w^2+39w+72=0

Solution for 5w^2+39w+72=0 equation:

Simplifying
5w2 + 39w + 72 = 0

Reorder the terms:
72 + 39w + 5w2 = 0

Solving
72 + 39w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(24 + 5w)(3 + w) = 0

Subproblem 1
Set the factor '(24 + 5w)' equal to zero and attempt to solve:

Simplifying
24 + 5w = 0

Solving
24 + 5w = 0

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

Add '-24' to each side of the equation.
24 + -24 + 5w = 0 + -24

Combine like terms: 24 + -24 = 0
0 + 5w = 0 + -24
5w = 0 + -24

Combine like terms: 0 + -24 = -24
5w = -24

Divide each side by '5'.
w = -4.8

Simplifying
w = -4.8
Subproblem 2
Set the factor '(3 + w)' equal to zero and attempt to solve:

Simplifying
3 + w = 0

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

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

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

Simplifying
w = -3
Solution
w = {-4.8, -3}