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

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

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

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

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

Combine like terms: 5w + 12w = 17w
(15 + 17w + 4w2) = 0

Solving
15 + 17w + 4w2 = 0

Solving for variable 'w'.

Factor a trinomial.
(3 + w)(5 + 4w) = 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 '(5 + 4w)' equal to zero and attempt to solve:

Simplifying
5 + 4w = 0

Solving
5 + 4w = 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 + 4w = 0 + -5

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

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

Divide each side by '4'.
w = -1.25

Simplifying
w = -1.25
Solution
w = {-3, -1.25}