3(2x+1)2(4x+2)=35

Solution for 3(2x+1)2(4x+2)=35 equation:

Simplifying
3(2x + 1) * 2(4x + 2) = 35

Reorder the terms:
3(1 + 2x) * 2(4x + 2) = 35

Reorder the terms:
3(1 + 2x) * 2(2 + 4x) = 35

Reorder the terms for easier multiplication:
3 * 2(1 + 2x)(2 + 4x) = 35

Multiply 3 * 2
6(1 + 2x)(2 + 4x) = 35

Multiply (1 + 2x) * (2 + 4x)
6(1(2 + 4x) + 2x * (2 + 4x)) = 35
6((2 * 1 + 4x * 1) + 2x * (2 + 4x)) = 35
6((2 + 4x) + 2x * (2 + 4x)) = 35
6(2 + 4x + (2 * 2x + 4x * 2x)) = 35
6(2 + 4x + (4x + 8x2)) = 35

Combine like terms: 4x + 4x = 8x
6(2 + 8x + 8x2) = 35
(2 * 6 + 8x * 6 + 8x2 * 6) = 35
(12 + 48x + 48x2) = 35

Solving
12 + 48x + 48x2 = 35

Solving for variable 'x'.

Reorder the terms:
12 + -35 + 48x + 48x2 = 35 + -35

Combine like terms: 12 + -35 = -23
-23 + 48x + 48x2 = 35 + -35

Combine like terms: 35 + -35 = 0
-23 + 48x + 48x2 = 0

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

Divide each side by '48'.
-0.4791666667 + x + x2 = 0

Move the constant term to the right:

Add '0.4791666667' to each side of the equation.
-0.4791666667 + x + 0.4791666667 + x2 = 0 + 0.4791666667

Reorder the terms:
-0.4791666667 + 0.4791666667 + x + x2 = 0 + 0.4791666667

Combine like terms: -0.4791666667 + 0.4791666667 = 0.0000000000
0.0000000000 + x + x2 = 0 + 0.4791666667
x + x2 = 0 + 0.4791666667

Combine like terms: 0 + 0.4791666667 = 0.4791666667
x + x2 = 0.4791666667

The x term is x.  Take half its coefficient (0.5).
Square it (0.25) and add it to both sides.

Add '0.25' to each side of the equation.
 + 0.25 + x2 = 0.4791666667 + 0.25

Combine like terms:  + 0.25 = 1.25
1.25 + x2 = 0.4791666667 + 0.25

Combine like terms: 0.4791666667 + 0.25 = 0.7291666667
1.25 + x2 = 0.7291666667

Factor a perfect square on the left side:
(x + 0.5)(x + 0.5) = 0.7291666667

Calculate the square root of the right side: 0.853912564

Break this problem into two subproblems by setting 
(x + 0.5) equal to 0.853912564 and -0.853912564.

Subproblem 1
x + 0.5 = 0.853912564

Simplifying
x + 0.5 = 0.853912564

Reorder the terms:
0.5 + x = 0.853912564

Solving
0.5 + x = 0.853912564

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = 0.853912564 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = 0.853912564 + -0.5
x = 0.853912564 + -0.5

Combine like terms: 0.853912564 + -0.5 = 0.353912564
x = 0.353912564

Simplifying
x = 0.353912564

Subproblem 2
x + 0.5 = -0.853912564

Simplifying
x + 0.5 = -0.853912564

Reorder the terms:
0.5 + x = -0.853912564

Solving
0.5 + x = -0.853912564

Solving for variable 'x'.

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

Add '-0.5' to each side of the equation.
0.5 + -0.5 + x = -0.853912564 + -0.5

Combine like terms: 0.5 + -0.5 = 0.0
0.0 + x = -0.853912564 + -0.5
x = -0.853912564 + -0.5

Combine like terms: -0.853912564 + -0.5 = -1.353912564
x = -1.353912564

Simplifying
x = -1.353912564

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.353912564, -1.353912564}