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

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

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

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

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

Multiply (3 + 2x) * (2 + x)
(3(2 + x) + 2x * (2 + x)) + -3(x + 2) = 0
((2 * 3 + x * 3) + 2x * (2 + x)) + -3(x + 2) = 0
((6 + 3x) + 2x * (2 + x)) + -3(x + 2) = 0
(6 + 3x + (2 * 2x + x * 2x)) + -3(x + 2) = 0
(6 + 3x + (4x + 2x2)) + -3(x + 2) = 0

Combine like terms: 3x + 4x = 7x
(6 + 7x + 2x2) + -3(x + 2) = 0

Reorder the terms:
6 + 7x + 2x2 + -3(2 + x) = 0
6 + 7x + 2x2 + (2 * -3 + x * -3) = 0
6 + 7x + 2x2 + (-6 + -3x) = 0

Reorder the terms:
6 + -6 + 7x + -3x + 2x2 = 0

Combine like terms: 6 + -6 = 0
0 + 7x + -3x + 2x2 = 0
7x + -3x + 2x2 = 0

Combine like terms: 7x + -3x = 4x
4x + 2x2 = 0

Solving
4x + 2x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x'.
2x(2 + x) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
Subproblem 2
Set the factor '(2 + x)' equal to zero and attempt to solve:

Simplifying
2 + x = 0

Solving
2 + x = 0

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

Add '-2' to each side of the equation.
2 + -2 + x = 0 + -2

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

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

Simplifying
x = -2
Solution
x = {0, -2}