(3+w)(5w+4)=0

Solution for (3+w)(5w+4)=0 equation:

Simplifying
(3 + w)(5w + 4) = 0

Reorder the terms:
(3 + w)(4 + 5w) = 0

Multiply (3 + w) * (4 + 5w)
(3(4 + 5w) + w(4 + 5w)) = 0
((4 * 3 + 5w * 3) + w(4 + 5w)) = 0
((12 + 15w) + w(4 + 5w)) = 0
(12 + 15w + (4 * w + 5w * w)) = 0
(12 + 15w + (4w + 5w2)) = 0

Combine like terms: 15w + 4w = 19w
(12 + 19w + 5w2) = 0

Solving
12 + 19w + 5w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + w)(4 + 5w) = 0

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

Simplifying
3 + w = 0

Solving
3 + w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-3' to each side of the equation.
3 + -3 + w = 0 + -3

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

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

Simplifying
w = -3
Subproblem 2
Set the factor '(4 + 5w)' equal to zero and attempt to solve:

Simplifying
4 + 5w = 0

Solving
4 + 5w = 0

Move all terms containing w to the left, all other terms to the right.

Add '-4' to each side of the equation.
4 + -4 + 5w = 0 + -4

Combine like terms: 4 + -4 = 0
0 + 5w = 0 + -4
5w = 0 + -4

Combine like terms: 0 + -4 = -4
5w = -4

Divide each side by '5'.
w = -0.8

Simplifying
w = -0.8
Solution
w = {-3, -0.8}