3(2x+4)8x=40

Solution for 3(2x+4)8x=40 equation:

Simplifying
3(2x + 4) * 8x = 40

Reorder the terms:
3(4 + 2x) * 8x = 40

Reorder the terms for easier multiplication:
3 * 8x(4 + 2x) = 40

Multiply 3 * 8
24x(4 + 2x) = 40
(4 * 24x + 2x * 24x) = 40
(96x + 48x2) = 40

Solving
96x + 48x2 = 40

Solving for variable 'x'.

Reorder the terms:
-40 + 96x + 48x2 = 40 + -40

Combine like terms: 40 + -40 = 0
-40 + 96x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(-5 + 12x + 6x2) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(-5 + 12x + 6x2)' equal to zero and attempt to solve:

Simplifying
-5 + 12x + 6x2 = 0

Solving
-5 + 12x + 6x2 = 0

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

Divide each side by '6'.
-0.8333333333 + 2x + x2 = 0

Move the constant term to the right:

Add '0.8333333333' to each side of the equation.
-0.8333333333 + 2x + 0.8333333333 + x2 = 0 + 0.8333333333

Reorder the terms:
-0.8333333333 + 0.8333333333 + 2x + x2 = 0 + 0.8333333333

Combine like terms: -0.8333333333 + 0.8333333333 = 0.0000000000
0.0000000000 + 2x + x2 = 0 + 0.8333333333
2x + x2 = 0 + 0.8333333333

Combine like terms: 0 + 0.8333333333 = 0.8333333333
2x + x2 = 0.8333333333

The x term is 2x.  Take half its coefficient (1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
2x + 1 + x2 = 0.8333333333 + 1

Reorder the terms:
1 + 2x + x2 = 0.8333333333 + 1

Combine like terms: 0.8333333333 + 1 = 1.8333333333
1 + 2x + x2 = 1.8333333333

Factor a perfect square on the left side:
(x + 1)(x + 1) = 1.8333333333

Calculate the square root of the right side: 1.354006401

Break this problem into two subproblems by setting 
(x + 1) equal to 1.354006401 and -1.354006401.

Subproblem 1
x + 1 = 1.354006401

Simplifying
x + 1 = 1.354006401

Reorder the terms:
1 + x = 1.354006401

Solving
1 + x = 1.354006401

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = 1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + x = 1.354006401 + -1
x = 1.354006401 + -1

Combine like terms: 1.354006401 + -1 = 0.354006401
x = 0.354006401

Simplifying
x = 0.354006401

Subproblem 2
x + 1 = -1.354006401

Simplifying
x + 1 = -1.354006401

Reorder the terms:
1 + x = -1.354006401

Solving
1 + x = -1.354006401

Solving for variable 'x'.

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

Add '-1' to each side of the equation.
1 + -1 + x = -1.354006401 + -1

Combine like terms: 1 + -1 = 0
0 + x = -1.354006401 + -1
x = -1.354006401 + -1

Combine like terms: -1.354006401 + -1 = -2.354006401
x = -2.354006401

Simplifying
x = -2.354006401

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.354006401, -2.354006401}
Solution
x = {0.354006401, -2.354006401}