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

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

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

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

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

Combine like terms: 15w + -2w = 13w
(6 + 13w + -5w2) = 0

Solving
6 + 13w + -5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + -1w)(2 + 5w) = 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 '(2 + 5w)' equal to zero and attempt to solve:

Simplifying
2 + 5w = 0

Solving
2 + 5w = 0

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

Add '-2' to each side of the equation.
2 + -2 + 5w = 0 + -2

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

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

Divide each side by '5'.
w = -0.4

Simplifying
w = -0.4
Solution
w = {3, -0.4}