w(2w+1)=55

Solution for w(2w+1)=55 equation:

Simplifying
w(2w + 1) = 55

Reorder the terms:
w(1 + 2w) = 55
(1 * w + 2w * w) = 55
(1w + 2w2) = 55

Solving
1w + 2w2 = 55

Solving for variable 'w'.

Reorder the terms:
-55 + 1w + 2w2 = 55 + -55

Combine like terms: 55 + -55 = 0
-55 + 1w + 2w2 = 0

Factor a trinomial.
(-11 + -2w)(5 + -1w) = 0

Subproblem 1
Set the factor '(-11 + -2w)' equal to zero and attempt to solve:

Simplifying
-11 + -2w = 0

Solving
-11 + -2w = 0

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

Add '11' to each side of the equation.
-11 + 11 + -2w = 0 + 11

Combine like terms: -11 + 11 = 0
0 + -2w = 0 + 11
-2w = 0 + 11

Combine like terms: 0 + 11 = 11
-2w = 11

Divide each side by '-2'.
w = -5.5

Simplifying
w = -5.5
Subproblem 2
Set the factor '(5 + -1w)' equal to zero and attempt to solve:

Simplifying
5 + -1w = 0

Solving
5 + -1w = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1w = 0 + -5
-1w = 0 + -5

Combine like terms: 0 + -5 = -5
-1w = -5

Divide each side by '-1'.
w = 5

Simplifying
w = 5
Solution
w = {-5.5, 5}