2w(4w+1)=3

Solution for 2w(4w+1)=3 equation:

Simplifying
2w(4w + 1) = 3

Reorder the terms:
2w(1 + 4w) = 3
(1 * 2w + 4w * 2w) = 3
(2w + 8w2) = 3

Solving
2w + 8w2 = 3

Solving for variable 'w'.

Reorder the terms:
-3 + 2w + 8w2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 2w + 8w2 = 0

Factor a trinomial.
(-3 + -4w)(1 + -2w) = 0

Subproblem 1
Set the factor '(-3 + -4w)' equal to zero and attempt to solve:

Simplifying
-3 + -4w = 0

Solving
-3 + -4w = 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 + -4w = 0 + 3

Combine like terms: -3 + 3 = 0
0 + -4w = 0 + 3
-4w = 0 + 3

Combine like terms: 0 + 3 = 3
-4w = 3

Divide each side by '-4'.
w = -0.75

Simplifying
w = -0.75
Subproblem 2
Set the factor '(1 + -2w)' equal to zero and attempt to solve:

Simplifying
1 + -2w = 0

Solving
1 + -2w = 0

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

Add '-1' to each side of the equation.
1 + -1 + -2w = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -2w = 0 + -1
-2w = 0 + -1

Combine like terms: 0 + -1 = -1
-2w = -1

Divide each side by '-2'.
w = 0.5

Simplifying
w = 0.5
Solution
w = {-0.75, 0.5}