(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 = 7w
(2 + 7w + 5w2) = 0

Solving
2 + 7w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(1 + w)(2 + 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 '(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}