7w^2+24w+9=0

Solution for 7w^2+24w+9=0 equation:

Simplifying
7w2 + 24w + 9 = 0

Reorder the terms:
9 + 24w + 7w2 = 0

Solving
9 + 24w + 7w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + w)(3 + 7w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(3 + 7w)' equal to zero and attempt to solve:

Simplifying
3 + 7w = 0

Solving
3 + 7w = 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 + 7w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 7w = 0 + -3
7w = 0 + -3

Combine like terms: 0 + -3 = -3
7w = -3

Divide each side by '7'.
w = -0.4285714286

Simplifying
w = -0.4285714286
Solution
w = {-3, -0.4285714286}