(2w-5)(1-w)=0

Solution for (2w-5)(1-w)=0 equation:

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

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

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

Combine like terms: 5w + 2w = 7w
(-5 + 7w + -2w2) = 0

Solving
-5 + 7w + -2w2 = 0

Solving for variable 'w'.

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

Subproblem 1
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
Subproblem 2
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
Solution
w = {2.5, 1}