8(x+2)3(x+3)=20

Solution for 8(x+2)3(x+3)=20 equation:

Simplifying
8(x + 2) * 3(x + 3) = 20

Reorder the terms:
8(2 + x) * 3(x + 3) = 20

Reorder the terms:
8(2 + x) * 3(3 + x) = 20

Reorder the terms for easier multiplication:
8 * 3(2 + x)(3 + x) = 20

Multiply 8 * 3
24(2 + x)(3 + x) = 20

Multiply (2 + x) * (3 + x)
24(2(3 + x) + x(3 + x)) = 20
24((3 * 2 + x * 2) + x(3 + x)) = 20
24((6 + 2x) + x(3 + x)) = 20
24(6 + 2x + (3 * x + x * x)) = 20
24(6 + 2x + (3x + x2)) = 20

Combine like terms: 2x + 3x = 5x
24(6 + 5x + x2) = 20
(6 * 24 + 5x * 24 + x2 * 24) = 20
(144 + 120x + 24x2) = 20

Solving
144 + 120x + 24x2 = 20

Solving for variable 'x'.

Reorder the terms:
144 + -20 + 120x + 24x2 = 20 + -20

Combine like terms: 144 + -20 = 124
124 + 120x + 24x2 = 20 + -20

Combine like terms: 20 + -20 = 0
124 + 120x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(31 + 30x + 6x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(31 + 30x + 6x2)' equal to zero and attempt to solve:

Simplifying
31 + 30x + 6x2 = 0

Solving
31 + 30x + 6x2 = 0

Begin completing the square.  Divide all terms by
6 the coefficient of the squared term: 

Divide each side by '6'.
5.166666667 + 5x + x2 = 0

Move the constant term to the right:

Add '-5.166666667' to each side of the equation.
5.166666667 + 5x + -5.166666667 + x2 = 0 + -5.166666667

Reorder the terms:
5.166666667 + -5.166666667 + 5x + x2 = 0 + -5.166666667

Combine like terms: 5.166666667 + -5.166666667 = 0.000000000
0.000000000 + 5x + x2 = 0 + -5.166666667
5x + x2 = 0 + -5.166666667

Combine like terms: 0 + -5.166666667 = -5.166666667
5x + x2 = -5.166666667

The x term is 5x.  Take half its coefficient (2.5).
Square it (6.25) and add it to both sides.

Add '6.25' to each side of the equation.
5x + 6.25 + x2 = -5.166666667 + 6.25

Reorder the terms:
6.25 + 5x + x2 = -5.166666667 + 6.25

Combine like terms: -5.166666667 + 6.25 = 1.083333333
6.25 + 5x + x2 = 1.083333333

Factor a perfect square on the left side:
(x + 2.5)(x + 2.5) = 1.083333333

Calculate the square root of the right side: 1.040833

Break this problem into two subproblems by setting 
(x + 2.5) equal to 1.040833 and -1.040833.

Subproblem 1
x + 2.5 = 1.040833

Simplifying
x + 2.5 = 1.040833

Reorder the terms:
2.5 + x = 1.040833

Solving
2.5 + x = 1.040833

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = 1.040833 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = 1.040833 + -2.5
x = 1.040833 + -2.5

Combine like terms: 1.040833 + -2.5 = -1.459167
x = -1.459167

Simplifying
x = -1.459167

Subproblem 2
x + 2.5 = -1.040833

Simplifying
x + 2.5 = -1.040833

Reorder the terms:
2.5 + x = -1.040833

Solving
2.5 + x = -1.040833

Solving for variable 'x'.

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

Add '-2.5' to each side of the equation.
2.5 + -2.5 + x = -1.040833 + -2.5

Combine like terms: 2.5 + -2.5 = 0.0
0.0 + x = -1.040833 + -2.5
x = -1.040833 + -2.5

Combine like terms: -1.040833 + -2.5 = -3.540833
x = -3.540833

Simplifying
x = -3.540833

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-1.459167, -3.540833}
Solution
x = {-1.459167, -3.540833}