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

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

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

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

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

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

Solving
-2 + 3w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(-1 + -1w)(2 + -5w) = 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 '(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 = {-1, 0.4}