w(w+1)+9(w+1)=0

Solution for w(w+1)+9(w+1)=0 equation:

Simplifying
w(w + 1) + 9(w + 1) = 0

Reorder the terms:
w(1 + w) + 9(w + 1) = 0
(1 * w + w * w) + 9(w + 1) = 0
(1w + w2) + 9(w + 1) = 0

Reorder the terms:
1w + w2 + 9(1 + w) = 0
1w + w2 + (1 * 9 + w * 9) = 0
1w + w2 + (9 + 9w) = 0

Reorder the terms:
9 + 1w + 9w + w2 = 0

Combine like terms: 1w + 9w = 10w
9 + 10w + w2 = 0

Solving
9 + 10w + w2 = 0

Solving for variable 'w'.

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

Subproblem 1
Set the factor '(9 + w)' equal to zero and attempt to solve:

Simplifying
9 + w = 0

Solving
9 + w = 0

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

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

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

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

Simplifying
w = -9
Subproblem 2
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
Solution
w = {-9, -1}