2w^2+9w+31=w^2-2w+1

Solution for 2w^2+9w+31=w^2-2w+1 equation:

Simplifying
2w2 + 9w + 31 = w2 + -2w + 1

Reorder the terms:
31 + 9w + 2w2 = w2 + -2w + 1

Reorder the terms:
31 + 9w + 2w2 = 1 + -2w + w2

Solving
31 + 9w + 2w2 = 1 + -2w + w2

Solving for variable 'w'.

Reorder the terms:
31 + -1 + 9w + 2w + 2w2 + -1w2 = 1 + -2w + w2 + -1 + 2w + -1w2

Combine like terms: 31 + -1 = 30
30 + 9w + 2w + 2w2 + -1w2 = 1 + -2w + w2 + -1 + 2w + -1w2

Combine like terms: 9w + 2w = 11w
30 + 11w + 2w2 + -1w2 = 1 + -2w + w2 + -1 + 2w + -1w2

Combine like terms: 2w2 + -1w2 = 1w2
30 + 11w + 1w2 = 1 + -2w + w2 + -1 + 2w + -1w2

Reorder the terms:
30 + 11w + 1w2 = 1 + -1 + -2w + 2w + w2 + -1w2

Combine like terms: 1 + -1 = 0
30 + 11w + 1w2 = 0 + -2w + 2w + w2 + -1w2
30 + 11w + 1w2 = -2w + 2w + w2 + -1w2

Combine like terms: -2w + 2w = 0
30 + 11w + 1w2 = 0 + w2 + -1w2
30 + 11w + 1w2 = w2 + -1w2

Combine like terms: w2 + -1w2 = 0
30 + 11w + 1w2 = 0

Factor a trinomial.
(6 + w)(5 + w) = 0

Subproblem 1
Set the factor '(6 + w)' equal to zero and attempt to solve:

Simplifying
6 + w = 0

Solving
6 + w = 0

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

Add '-6' to each side of the equation.
6 + -6 + w = 0 + -6

Combine like terms: 6 + -6 = 0
0 + w = 0 + -6
w = 0 + -6

Combine like terms: 0 + -6 = -6
w = -6

Simplifying
w = -6
Subproblem 2
Set the factor '(5 + w)' equal to zero and attempt to solve:

Simplifying
5 + w = 0

Solving
5 + w = 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 + w = 0 + -5

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

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

Simplifying
w = -5
Solution
w = {-6, -5}