2(x+3)3(x+1)=24

Solution for 2(x+3)3(x+1)=24 equation:

Simplifying
2(x + 3) * 3(x + 1) = 24

Reorder the terms:
2(3 + x) * 3(x + 1) = 24

Reorder the terms:
2(3 + x) * 3(1 + x) = 24

Reorder the terms for easier multiplication:
2 * 3(3 + x)(1 + x) = 24

Multiply 2 * 3
6(3 + x)(1 + x) = 24

Multiply (3 + x) * (1 + x)
6(3(1 + x) + x(1 + x)) = 24
6((1 * 3 + x * 3) + x(1 + x)) = 24
6((3 + 3x) + x(1 + x)) = 24
6(3 + 3x + (1 * x + x * x)) = 24
6(3 + 3x + (1x + x2)) = 24

Combine like terms: 3x + 1x = 4x
6(3 + 4x + x2) = 24
(3 * 6 + 4x * 6 + x2 * 6) = 24
(18 + 24x + 6x2) = 24

Solving
18 + 24x + 6x2 = 24

Solving for variable 'x'.

Reorder the terms:
18 + -24 + 24x + 6x2 = 24 + -24

Combine like terms: 18 + -24 = -6
-6 + 24x + 6x2 = 24 + -24

Combine like terms: 24 + -24 = 0
-6 + 24x + 6x2 = 0

Factor out the Greatest Common Factor (GCF), '6'.
6(-1 + 4x + x2) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-1 + 4x + x2)' equal to zero and attempt to solve:

Simplifying
-1 + 4x + x2 = 0

Solving
-1 + 4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + 4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + 4x + x2 = 0 + 1

Combine like terms: -1 + 1 = 0
0 + 4x + x2 = 0 + 1
4x + x2 = 0 + 1

Combine like terms: 0 + 1 = 1
4x + x2 = 1

The x term is 4x.  Take half its coefficient (2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
4x + 4 + x2 = 1 + 4

Reorder the terms:
4 + 4x + x2 = 1 + 4

Combine like terms: 1 + 4 = 5
4 + 4x + x2 = 5

Factor a perfect square on the left side:
(x + 2)(x + 2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + 2) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + 2 = 2.236067978

Simplifying
x + 2 = 2.236067978

Reorder the terms:
2 + x = 2.236067978

Solving
2 + x = 2.236067978

Solving for variable 'x'.

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 = 2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + x = 2.236067978 + -2
x = 2.236067978 + -2

Combine like terms: 2.236067978 + -2 = 0.236067978
x = 0.236067978

Simplifying
x = 0.236067978

Subproblem 2
x + 2 = -2.236067978

Simplifying
x + 2 = -2.236067978

Reorder the terms:
2 + x = -2.236067978

Solving
2 + x = -2.236067978

Solving for variable 'x'.

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 = -2.236067978 + -2

Combine like terms: 2 + -2 = 0
0 + x = -2.236067978 + -2
x = -2.236067978 + -2

Combine like terms: -2.236067978 + -2 = -4.236067978
x = -4.236067978

Simplifying
x = -4.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.236067978, -4.236067978}
Solution
x = {0.236067978, -4.236067978}