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

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

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

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

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

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

Combine like terms: 2x + 3x = 5x
(6 + 5x + x2) = 6

Add '-6' to each side of the equation.
6 + 5x + -6 + x2 = 6 + -6

Reorder the terms:
6 + -6 + 5x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
0 + 5x + x2 = 6 + -6
5x + x2 = 6 + -6

Combine like terms: 6 + -6 = 0
5x + x2 = 0

Solving
5x + x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), 'x'.
x(5 + x) = 0

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 '(5 + x)' equal to zero and attempt to solve:

Simplifying
5 + x = 0

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

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

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

Simplifying
x = -5
Solution
x = {0, -5}