10w^2+11w+1=0

Solution for 10w^2+11w+1=0 equation:

Simplifying
10w2 + 11w + 1 = 0

Reorder the terms:
1 + 11w + 10w2 = 0

Solving
1 + 11w + 10w2 = 0

Solving for variable 'w'.

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

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

Simplifying
1 + w = 0

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

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

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

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

Simplifying
1 + 10w = 0

Solving
1 + 10w = 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 + 10w = 0 + -1

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

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

Divide each side by '10'.
w = -0.1

Simplifying
w = -0.1
Solution
w = {-1, -0.1}