(2w+9)(1+w)=0

Solution for (2w+9)(1+w)=0 equation:

Simplifying
(2w + 9)(1 + w) = 0

Reorder the terms:
(9 + 2w)(1 + w) = 0

Multiply (9 + 2w) * (1 + w)
(9(1 + w) + 2w * (1 + w)) = 0
((1 * 9 + w * 9) + 2w * (1 + w)) = 0
((9 + 9w) + 2w * (1 + w)) = 0
(9 + 9w + (1 * 2w + w * 2w)) = 0
(9 + 9w + (2w + 2w2)) = 0

Combine like terms: 9w + 2w = 11w
(9 + 11w + 2w2) = 0

Solving
9 + 11w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(9 + 2w)(1 + w) = 0

Subproblem 1
Set the factor '(9 + 2w)' equal to zero and attempt to solve:

Simplifying
9 + 2w = 0

Solving
9 + 2w = 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 + 2w = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 2w = 0 + -9
2w = 0 + -9

Combine like terms: 0 + -9 = -9
2w = -9

Divide each side by '2'.
w = -4.5

Simplifying
w = -4.5
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 = {-4.5, -1}