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

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

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

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

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

Combine like terms: 2w + -5w = -3w
(-5 + -3w + 2w2) = 0

Solving
-5 + -3w + 2w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(5 + -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 '(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 = {-1, 2.5}