(x+1)(4x+2)=656

Solution for (x+1)(4x+2)=656 equation:

Simplifying
(x + 1)(4x + 2) = 656

Reorder the terms:
(1 + x)(4x + 2) = 656

Reorder the terms:
(1 + x)(2 + 4x) = 656

Multiply (1 + x) * (2 + 4x)
(1(2 + 4x) + x(2 + 4x)) = 656
((2 * 1 + 4x * 1) + x(2 + 4x)) = 656
((2 + 4x) + x(2 + 4x)) = 656
(2 + 4x + (2 * x + 4x * x)) = 656
(2 + 4x + (2x + 4x2)) = 656

Combine like terms: 4x + 2x = 6x
(2 + 6x + 4x2) = 656

Solving
2 + 6x + 4x2 = 656

Solving for variable 'x'.

Reorder the terms:
2 + -656 + 6x + 4x2 = 656 + -656

Combine like terms: 2 + -656 = -654
-654 + 6x + 4x2 = 656 + -656

Combine like terms: 656 + -656 = 0
-654 + 6x + 4x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-327 + 3x + 2x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-327 + 3x + 2x2)' equal to zero and attempt to solve:

Simplifying
-327 + 3x + 2x2 = 0

Solving
-327 + 3x + 2x2 = 0

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

Divide each side by '2'.
-163.5 + 1.5x + x2 = 0

Move the constant term to the right:

Add '163.5' to each side of the equation.
-163.5 + 1.5x + 163.5 + x2 = 0 + 163.5

Reorder the terms:
-163.5 + 163.5 + 1.5x + x2 = 0 + 163.5

Combine like terms: -163.5 + 163.5 = 0.0
0.0 + 1.5x + x2 = 0 + 163.5
1.5x + x2 = 0 + 163.5

Combine like terms: 0 + 163.5 = 163.5
1.5x + x2 = 163.5

The x term is 1.5x.  Take half its coefficient (0.75).
Square it (0.5625) and add it to both sides.

Add '0.5625' to each side of the equation.
1.5x + 0.5625 + x2 = 163.5 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = 163.5 + 0.5625

Combine like terms: 163.5 + 0.5625 = 164.0625
0.5625 + 1.5x + x2 = 164.0625

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 164.0625

Calculate the square root of the right side: 12.808688457

Break this problem into two subproblems by setting 
(x + 0.75) equal to 12.808688457 and -12.808688457.

Subproblem 1
x + 0.75 = 12.808688457

Simplifying
x + 0.75 = 12.808688457

Reorder the terms:
0.75 + x = 12.808688457

Solving
0.75 + x = 12.808688457

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = 12.808688457 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 12.808688457 + -0.75
x = 12.808688457 + -0.75

Combine like terms: 12.808688457 + -0.75 = 12.058688457
x = 12.058688457

Simplifying
x = 12.058688457

Subproblem 2
x + 0.75 = -12.808688457

Simplifying
x + 0.75 = -12.808688457

Reorder the terms:
0.75 + x = -12.808688457

Solving
0.75 + x = -12.808688457

Solving for variable 'x'.

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

Add '-0.75' to each side of the equation.
0.75 + -0.75 + x = -12.808688457 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -12.808688457 + -0.75
x = -12.808688457 + -0.75

Combine like terms: -12.808688457 + -0.75 = -13.558688457
x = -13.558688457

Simplifying
x = -13.558688457

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {12.058688457, -13.558688457}
Solution
x = {12.058688457, -13.558688457}