8w^2+26w+21=0

Solution for 8w^2+26w+21=0 equation:

Simplifying
8w2 + 26w + 21 = 0

Reorder the terms:
21 + 26w + 8w2 = 0

Solving
21 + 26w + 8w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(7 + 4w)(3 + 2w) = 0

Subproblem 1
Set the factor '(7 + 4w)' equal to zero and attempt to solve:

Simplifying
7 + 4w = 0

Solving
7 + 4w = 0

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

Add '-7' to each side of the equation.
7 + -7 + 4w = 0 + -7

Combine like terms: 7 + -7 = 0
0 + 4w = 0 + -7
4w = 0 + -7

Combine like terms: 0 + -7 = -7
4w = -7

Divide each side by '4'.
w = -1.75

Simplifying
w = -1.75
Subproblem 2
Set the factor '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 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 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {-1.75, -1.5}