w(11w+1)=10

Solution for w(11w+1)=10 equation:

Simplifying
w(11w + 1) = 10

Reorder the terms:
w(1 + 11w) = 10
(1 * w + 11w * w) = 10
(1w + 11w2) = 10

Solving
1w + 11w2 = 10

Solving for variable 'w'.

Reorder the terms:
-10 + 1w + 11w2 = 10 + -10

Combine like terms: 10 + -10 = 0
-10 + 1w + 11w2 = 0

Factor a trinomial.
(-1 + -1w)(10 + -11w) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(10 + -11w)' equal to zero and attempt to solve:

Simplifying
10 + -11w = 0

Solving
10 + -11w = 0

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

Add '-10' to each side of the equation.
10 + -10 + -11w = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -11w = 0 + -10
-11w = 0 + -10

Combine like terms: 0 + -10 = -10
-11w = -10

Divide each side by '-11'.
w = 0.9090909091

Simplifying
w = 0.9090909091
Solution
w = {-1, 0.9090909091}