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

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

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

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

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

Combine like terms: 12x + 3x = 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}