10w^2+24w+8=0

Solution for 10w^2+24w+8=0 equation:

Simplifying
10w2 + 24w + 8 = 0

Reorder the terms:
8 + 24w + 10w2 = 0

Solving
8 + 24w + 10w2 = 0

Solving for variable 'w'.

Factor out the Greatest Common Factor (GCF), '2'.
2(4 + 12w + 5w2) = 0

Factor a trinomial.
2((2 + w)(2 + 5w)) = 0

Ignore the factor 2.
Subproblem 1
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
Subproblem 2
Set the factor '(2 + 5w)' equal to zero and attempt to solve:

Simplifying
2 + 5w = 0

Solving
2 + 5w = 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 + 5w = 0 + -2

Combine like terms: 2 + -2 = 0
0 + 5w = 0 + -2
5w = 0 + -2

Combine like terms: 0 + -2 = -2
5w = -2

Divide each side by '5'.
w = -0.4

Simplifying
w = -0.4
Solution
w = {-2, -0.4}