24w+45=-3w^2

Solution for 24w+45=-3w^2 equation:

Simplifying
24w + 45 = -3w2

Reorder the terms:
45 + 24w = -3w2

Solving
45 + 24w = -3w2

Solving for variable 'w'.

Combine like terms: -3w2 + 3w2 = 0
45 + 24w + 3w2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(15 + 8w + w2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 0

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

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

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

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

Simplifying
w = -5
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 = {-5, -3}