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

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

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

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

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

Multiply (3 + 2x) * (3 + x)
(3(3 + x) + 2x * (3 + x)) = 0
((3 * 3 + x * 3) + 2x * (3 + x)) = 0
((9 + 3x) + 2x * (3 + x)) = 0
(9 + 3x + (3 * 2x + x * 2x)) = 0
(9 + 3x + (6x + 2x2)) = 0

Combine like terms: 3x + 6x = 9x
(9 + 9x + 2x2) = 0

Solving
9 + 9x + 2x2 = 0

Solving for variable 'x'.

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

Simplifying
3 + 2x = 0

Solving
3 + 2x = 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 + 2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2x = 0 + -3
2x = 0 + -3

Combine like terms: 0 + -3 = -3
2x = -3

Divide each side by '2'.
x = -1.5

Simplifying
x = -1.5
Solution
x = {-3, -1.5}