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

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

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

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

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

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

Solving
5 + 8w + 3w2 = 0

Solving for variable 'w'.

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

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

Simplifying
5 + 3w = 0

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

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

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

Divide each side by '3'.
w = -1.666666667

Simplifying
w = -1.666666667
Subproblem 2
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
Solution
w = {-1.666666667, -1}