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

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

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

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

Multiply (3 + 4w) * (5 + w)
(3(5 + w) + 4w * (5 + w)) = 0
((5 * 3 + w * 3) + 4w * (5 + w)) = 0
((15 + 3w) + 4w * (5 + w)) = 0
(15 + 3w + (5 * 4w + w * 4w)) = 0
(15 + 3w + (20w + 4w2)) = 0

Combine like terms: 3w + 20w = 23w
(15 + 23w + 4w2) = 0

Solving
15 + 23w + 4w2 = 0

Solving for variable 'w'.

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

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

Simplifying
5 + w = 0

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

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

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

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

Simplifying
3 + 4w = 0

Solving
3 + 4w = 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 + 4w = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 4w = 0 + -3
4w = 0 + -3

Combine like terms: 0 + -3 = -3
4w = -3

Divide each side by '4'.
w = -0.75

Simplifying
w = -0.75
Solution
w = {-5, -0.75}