(x+3)(2x+5)=0

Solution for (x+3)(2x+5)=0 equation:

Simplifying
(x + 3)(2x + 5) = 0

Reorder the terms:
(3 + x)(2x + 5) = 0

Reorder the terms:
(3 + x)(5 + 2x) = 0

Multiply (3 + x) * (5 + 2x)
(3(5 + 2x) + x(5 + 2x)) = 0
((5 * 3 + 2x * 3) + x(5 + 2x)) = 0
((15 + 6x) + x(5 + 2x)) = 0
(15 + 6x + (5 * x + 2x * x)) = 0
(15 + 6x + (5x + 2x2)) = 0

Combine like terms: 6x + 5x = 11x
(15 + 11x + 2x2) = 0

Solving
15 + 11x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(3 + x)(5 + 2x) = 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 + 2x)' equal to zero and attempt to solve:

Simplifying
5 + 2x = 0

Solving
5 + 2x = 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 + 2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 2x = 0 + -5
2x = 0 + -5

Combine like terms: 0 + -5 = -5
2x = -5

Divide each side by '2'.
x = -2.5

Simplifying
x = -2.5
Solution
x = {-3, -2.5}