(3-w)(2w+5)=0

Solution for (3-w)(2w+5)=0 equation:

Simplifying
(3 + -1w)(2w + 5) = 0

Reorder the terms:
(3 + -1w)(5 + 2w) = 0

Multiply (3 + -1w) * (5 + 2w)
(3(5 + 2w) + -1w * (5 + 2w)) = 0
((5 * 3 + 2w * 3) + -1w * (5 + 2w)) = 0
((15 + 6w) + -1w * (5 + 2w)) = 0
(15 + 6w + (5 * -1w + 2w * -1w)) = 0
(15 + 6w + (-5w + -2w2)) = 0

Combine like terms: 6w + -5w = 1w
(15 + 1w + -2w2) = 0

Solving
15 + 1w + -2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + -1w)(5 + 2w) = 0

Subproblem 1
Set the factor '(3 + -1w)' equal to zero and attempt to solve:

Simplifying
3 + -1w = 0

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

Combine like terms: 3 + -3 = 0
0 + -1w = 0 + -3
-1w = 0 + -3

Combine like terms: 0 + -3 = -3
-1w = -3

Divide each side by '-1'.
w = 3

Simplifying
w = 3
Subproblem 2
Set the factor '(5 + 2w)' equal to zero and attempt to solve:

Simplifying
5 + 2w = 0

Solving
5 + 2w = 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 + 2w = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2w = 0 + -5
2w = 0 + -5

Combine like terms: 0 + -5 = -5
2w = -5

Divide each side by '2'.
w = -2.5

Simplifying
w = -2.5
Solution
w = {3, -2.5}