(1-w)(2w+3)=0

Solution for (1-w)(2w+3)=0 equation:

Simplifying
(1 + -1w)(2w + 3) = 0

Reorder the terms:
(1 + -1w)(3 + 2w) = 0

Multiply (1 + -1w) * (3 + 2w)
(1(3 + 2w) + -1w * (3 + 2w)) = 0
((3 * 1 + 2w * 1) + -1w * (3 + 2w)) = 0
((3 + 2w) + -1w * (3 + 2w)) = 0
(3 + 2w + (3 * -1w + 2w * -1w)) = 0
(3 + 2w + (-3w + -2w2)) = 0

Combine like terms: 2w + -3w = -1w
(3 + -1w + -2w2) = 0

Solving
3 + -1w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + -1w)(3 + 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 '(3 + 2w)' equal to zero and attempt to solve:

Simplifying
3 + 2w = 0

Solving
3 + 2w = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2w = 0 + -3
2w = 0 + -3

Combine like terms: 0 + -3 = -3
2w = -3

Divide each side by '2'.
w = -1.5

Simplifying
w = -1.5
Solution
w = {1, -1.5}