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

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

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

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

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

Combine like terms: 2w + -9w = -7w
(-9 + -7w + 2w2) = 0

Solving
-9 + -7w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(9 + -2w) = 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 '(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
Solution
w = {-1, 4.5}