5(x+2)4(x+2)=3(x+8)+12

Solution for 5(x+2)4(x+2)=3(x+8)+12 equation:

Simplifying
5(x + 2) * 4(x + 2) = 3(x + 8) + 12

Reorder the terms:
5(2 + x) * 4(x + 2) = 3(x + 8) + 12

Reorder the terms:
5(2 + x) * 4(2 + x) = 3(x + 8) + 12

Reorder the terms for easier multiplication:
5 * 4(2 + x)(2 + x) = 3(x + 8) + 12

Multiply 5 * 4
20(2 + x)(2 + x) = 3(x + 8) + 12

Multiply (2 + x) * (2 + x)
20(2(2 + x) + x(2 + x)) = 3(x + 8) + 12
20((2 * 2 + x * 2) + x(2 + x)) = 3(x + 8) + 12
20((4 + 2x) + x(2 + x)) = 3(x + 8) + 12
20(4 + 2x + (2 * x + x * x)) = 3(x + 8) + 12
20(4 + 2x + (2x + x2)) = 3(x + 8) + 12

Combine like terms: 2x + 2x = 4x
20(4 + 4x + x2) = 3(x + 8) + 12
(4 * 20 + 4x * 20 + x2 * 20) = 3(x + 8) + 12
(80 + 80x + 20x2) = 3(x + 8) + 12

Reorder the terms:
80 + 80x + 20x2 = 3(8 + x) + 12
80 + 80x + 20x2 = (8 * 3 + x * 3) + 12
80 + 80x + 20x2 = (24 + 3x) + 12

Reorder the terms:
80 + 80x + 20x2 = 24 + 12 + 3x

Combine like terms: 24 + 12 = 36
80 + 80x + 20x2 = 36 + 3x

Solving
80 + 80x + 20x2 = 36 + 3x

Solving for variable 'x'.

Reorder the terms:
80 + -36 + 80x + -3x + 20x2 = 36 + 3x + -36 + -3x

Combine like terms: 80 + -36 = 44
44 + 80x + -3x + 20x2 = 36 + 3x + -36 + -3x

Combine like terms: 80x + -3x = 77x
44 + 77x + 20x2 = 36 + 3x + -36 + -3x

Reorder the terms:
44 + 77x + 20x2 = 36 + -36 + 3x + -3x

Combine like terms: 36 + -36 = 0
44 + 77x + 20x2 = 0 + 3x + -3x
44 + 77x + 20x2 = 3x + -3x

Combine like terms: 3x + -3x = 0
44 + 77x + 20x2 = 0

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

Divide each side by '20'.
2.2 + 3.85x + x2 = 0.0

Move the constant term to the right:

Add '-2.2' to each side of the equation.
2.2 + 3.85x + -2.2 + x2 = 0.0 + -2.2

Reorder the terms:
2.2 + -2.2 + 3.85x + x2 = 0.0 + -2.2

Combine like terms: 2.2 + -2.2 = 0.0
0.0 + 3.85x + x2 = 0.0 + -2.2
3.85x + x2 = 0.0 + -2.2

Combine like terms: 0.0 + -2.2 = -2.2
3.85x + x2 = -2.2

The x term is 3.85x.  Take half its coefficient (1.925).
Square it (3.705625) and add it to both sides.

Add '3.705625' to each side of the equation.
3.85x + 3.705625 + x2 = -2.2 + 3.705625

Reorder the terms:
3.705625 + 3.85x + x2 = -2.2 + 3.705625

Combine like terms: -2.2 + 3.705625 = 1.505625
3.705625 + 3.85x + x2 = 1.505625

Factor a perfect square on the left side:
(x + 1.925)(x + 1.925) = 1.505625

Calculate the square root of the right side: 1.227039119

Break this problem into two subproblems by setting 
(x + 1.925) equal to 1.227039119 and -1.227039119.

Subproblem 1
x + 1.925 = 1.227039119

Simplifying
x + 1.925 = 1.227039119

Reorder the terms:
1.925 + x = 1.227039119

Solving
1.925 + x = 1.227039119

Solving for variable 'x'.

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

Add '-1.925' to each side of the equation.
1.925 + -1.925 + x = 1.227039119 + -1.925

Combine like terms: 1.925 + -1.925 = 0.000
0.000 + x = 1.227039119 + -1.925
x = 1.227039119 + -1.925

Combine like terms: 1.227039119 + -1.925 = -0.697960881
x = -0.697960881

Simplifying
x = -0.697960881

Subproblem 2
x + 1.925 = -1.227039119

Simplifying
x + 1.925 = -1.227039119

Reorder the terms:
1.925 + x = -1.227039119

Solving
1.925 + x = -1.227039119

Solving for variable 'x'.

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

Add '-1.925' to each side of the equation.
1.925 + -1.925 + x = -1.227039119 + -1.925

Combine like terms: 1.925 + -1.925 = 0.000
0.000 + x = -1.227039119 + -1.925
x = -1.227039119 + -1.925

Combine like terms: -1.227039119 + -1.925 = -3.152039119
x = -3.152039119

Simplifying
x = -3.152039119

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.697960881, -3.152039119}