6w^2+48w+72=0

Solution for 6w^2+48w+72=0 equation:

Simplifying
6w2 + 48w + 72 = 0

Reorder the terms:
72 + 48w + 6w2 = 0

Solving
72 + 48w + 6w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '6'.
6(12 + 8w + w2) = 0

Factor a trinomial.
6((6 + w)(2 + w)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 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 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(2 + w)' equal to zero and attempt to solve:

Simplifying
2 + w = 0

Solving
2 + w = 0

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

Add '-2' to each side of the equation.
2 + -2 + w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + w = 0 + -2
w = 0 + -2

Combine like terms: 0 + -2 = -2
w = -2

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