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

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

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

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

Multiply (5 + 4x) * (3 + x)
(5(3 + x) + 4x * (3 + x)) = 0
((3 * 5 + x * 5) + 4x * (3 + x)) = 0
((15 + 5x) + 4x * (3 + x)) = 0
(15 + 5x + (3 * 4x + x * 4x)) = 0
(15 + 5x + (12x + 4x2)) = 0

Combine like terms: 5x + 12x = 17x
(15 + 17x + 4x2) = 0

Solving
15 + 17x + 4x2 = 0

Solving for variable 'x'.

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

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

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

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

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

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

Simplifying
5 + 4x = 0

Solving
5 + 4x = 0

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

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

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

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

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

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