30w+72=-3w^2

Solution for 30w+72=-3w^2 equation:

Simplifying
30w + 72 = -3w2

Reorder the terms:
72 + 30w = -3w2

Solving
72 + 30w = -3w2

Solving for variable 'w'.

Combine like terms: -3w2 + 3w2 = 0
72 + 30w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(24 + 10w + w2) = 0

Factor a trinomial.
3((6 + w)(4 + w)) = 0

Ignore the factor 3.
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 '(4 + w)' equal to zero and attempt to solve:

Simplifying
4 + w = 0

Solving
4 + w = 0

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

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

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

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

Simplifying
w = -4
Solution
w = {-6, -4}