w(2w+1)=3

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

Simplifying
w(2w + 1) = 3

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

Solving
1w + 2w2 = 3

Solving for variable 'w'.

Reorder the terms:
-3 + 1w + 2w2 = 3 + -3

Combine like terms: 3 + -3 = 0
-3 + 1w + 2w2 = 0

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

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

Simplifying
1 + -1w = 0

Solving
1 + -1w = 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 + -1w = 0 + -1

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

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

Divide each side by '-1'.
w = 1

Simplifying
w = 1
Solution
w = {-1.5, 1}