(1-w)(5w-3)=0

Solution for (1-w)(5w-3)=0 equation:

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

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

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

Combine like terms: 5w + 3w = 8w
(-3 + 8w + -5w2) = 0

Solving
-3 + 8w + -5w2 = 0

Solving for variable 'w'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(3 + -5w)' equal to zero and attempt to solve:

Simplifying
3 + -5w = 0

Solving
3 + -5w = 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 + -5w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -5w = 0 + -3
-5w = 0 + -3

Combine like terms: 0 + -3 = -3
-5w = -3

Divide each side by '-5'.
w = 0.6

Simplifying
w = 0.6
Solution
w = {1, 0.6}