(2x+3)(x+6)=0

Solution for (2x+3)(x+6)=0 equation:

Simplifying
(2x + 3)(x + 6) = 0

Reorder the terms:
(3 + 2x)(x + 6) = 0

Reorder the terms:
(3 + 2x)(6 + x) = 0

Multiply (3 + 2x) * (6 + x)
(3(6 + x) + 2x * (6 + x)) = 0
((6 * 3 + x * 3) + 2x * (6 + x)) = 0
((18 + 3x) + 2x * (6 + x)) = 0
(18 + 3x + (6 * 2x + x * 2x)) = 0
(18 + 3x + (12x + 2x2)) = 0

Combine like terms: 3x + 12x = 15x
(18 + 15x + 2x2) = 0

Solving
18 + 15x + 2x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6 + x)(3 + 2x) = 0

Subproblem 1
Set the factor '(6 + x)' equal to zero and attempt to solve:

Simplifying
6 + x = 0

Solving
6 + x = 0

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

Add '-6' to each side of the equation.
6 + -6 + x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + x = 0 + -6
x = 0 + -6

Combine like terms: 0 + -6 = -6
x = -6

Simplifying
x = -6
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 = {-6, -1.5}