w(9w+1)=8

Solution for w(9w+1)=8 equation:

Simplifying
w(9w + 1) = 8

Reorder the terms:
w(1 + 9w) = 8
(1 * w + 9w * w) = 8
(1w + 9w2) = 8

Solving
1w + 9w2 = 8

Solving for variable 'w'.

Reorder the terms:
-8 + 1w + 9w2 = 8 + -8

Combine like terms: 8 + -8 = 0
-8 + 1w + 9w2 = 0

Factor a trinomial.
(-1 + -1w)(8 + -9w) = 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 '(8 + -9w)' equal to zero and attempt to solve:

Simplifying
8 + -9w = 0

Solving
8 + -9w = 0

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

Add '-8' to each side of the equation.
8 + -8 + -9w = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -9w = 0 + -8
-9w = 0 + -8

Combine like terms: 0 + -8 = -8
-9w = -8

Divide each side by '-9'.
w = 0.8888888889

Simplifying
w = 0.8888888889
Solution
w = {-1, 0.8888888889}