(4x+1)(4x+1)=20

Solution for (4x+1)(4x+1)=20 equation:

Simplifying
(4x + 1)(4x + 1) = 20

Reorder the terms:
(1 + 4x)(4x + 1) = 20

Reorder the terms:
(1 + 4x)(1 + 4x) = 20

Multiply (1 + 4x) * (1 + 4x)
(1(1 + 4x) + 4x * (1 + 4x)) = 20
((1 * 1 + 4x * 1) + 4x * (1 + 4x)) = 20
((1 + 4x) + 4x * (1 + 4x)) = 20
(1 + 4x + (1 * 4x + 4x * 4x)) = 20
(1 + 4x + (4x + 16x2)) = 20

Combine like terms: 4x + 4x = 8x
(1 + 8x + 16x2) = 20

Solving
1 + 8x + 16x2 = 20

Solving for variable 'x'.

Reorder the terms:
1 + -20 + 8x + 16x2 = 20 + -20

Combine like terms: 1 + -20 = -19
-19 + 8x + 16x2 = 20 + -20

Combine like terms: 20 + -20 = 0
-19 + 8x + 16x2 = 0

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

Divide each side by '16'.
-1.1875 + 0.5x + x2 = 0

Move the constant term to the right:

Add '1.1875' to each side of the equation.
-1.1875 + 0.5x + 1.1875 + x2 = 0 + 1.1875

Reorder the terms:
-1.1875 + 1.1875 + 0.5x + x2 = 0 + 1.1875

Combine like terms: -1.1875 + 1.1875 = 0.0000
0.0000 + 0.5x + x2 = 0 + 1.1875
0.5x + x2 = 0 + 1.1875

Combine like terms: 0 + 1.1875 = 1.1875
0.5x + x2 = 1.1875

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 1.1875 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 1.1875 + 0.0625

Combine like terms: 1.1875 + 0.0625 = 1.25
0.0625 + 0.5x + x2 = 1.25

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 1.25

Calculate the square root of the right side: 1.118033989

Break this problem into two subproblems by setting 
(x + 0.25) equal to 1.118033989 and -1.118033989.

Subproblem 1
x + 0.25 = 1.118033989

Simplifying
x + 0.25 = 1.118033989

Reorder the terms:
0.25 + x = 1.118033989

Solving
0.25 + x = 1.118033989

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 1.118033989 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 1.118033989 + -0.25
x = 1.118033989 + -0.25

Combine like terms: 1.118033989 + -0.25 = 0.868033989
x = 0.868033989

Simplifying
x = 0.868033989

Subproblem 2
x + 0.25 = -1.118033989

Simplifying
x + 0.25 = -1.118033989

Reorder the terms:
0.25 + x = -1.118033989

Solving
0.25 + x = -1.118033989

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -1.118033989 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -1.118033989 + -0.25
x = -1.118033989 + -0.25

Combine like terms: -1.118033989 + -0.25 = -1.368033989
x = -1.368033989

Simplifying
x = -1.368033989

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.868033989, -1.368033989}