(4x+3)(4x+3)=7

Solution for (4x+3)(4x+3)=7 equation:

Simplifying
(4x + 3)(4x + 3) = 7

Reorder the terms:
(3 + 4x)(4x + 3) = 7

Reorder the terms:
(3 + 4x)(3 + 4x) = 7

Multiply (3 + 4x) * (3 + 4x)
(3(3 + 4x) + 4x * (3 + 4x)) = 7
((3 * 3 + 4x * 3) + 4x * (3 + 4x)) = 7
((9 + 12x) + 4x * (3 + 4x)) = 7
(9 + 12x + (3 * 4x + 4x * 4x)) = 7
(9 + 12x + (12x + 16x2)) = 7

Combine like terms: 12x + 12x = 24x
(9 + 24x + 16x2) = 7

Solving
9 + 24x + 16x2 = 7

Solving for variable 'x'.

Reorder the terms:
9 + -7 + 24x + 16x2 = 7 + -7

Combine like terms: 9 + -7 = 2
2 + 24x + 16x2 = 7 + -7

Combine like terms: 7 + -7 = 0
2 + 24x + 16x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(1 + 12x + 8x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(1 + 12x + 8x2)' equal to zero and attempt to solve:

Simplifying
1 + 12x + 8x2 = 0

Solving
1 + 12x + 8x2 = 0

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

Divide each side by '8'.
0.125 + 1.5x + x2 = 0

Move the constant term to the right:

Add '-0.125' to each side of the equation.
0.125 + 1.5x + -0.125 + x2 = 0 + -0.125

Reorder the terms:
0.125 + -0.125 + 1.5x + x2 = 0 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + 1.5x + x2 = 0 + -0.125
1.5x + x2 = 0 + -0.125

Combine like terms: 0 + -0.125 = -0.125
1.5x + x2 = -0.125

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 = -0.125 + 0.5625

Reorder the terms:
0.5625 + 1.5x + x2 = -0.125 + 0.5625

Combine like terms: -0.125 + 0.5625 = 0.4375
0.5625 + 1.5x + x2 = 0.4375

Factor a perfect square on the left side:
(x + 0.75)(x + 0.75) = 0.4375

Calculate the square root of the right side: 0.661437828

Break this problem into two subproblems by setting 
(x + 0.75) equal to 0.661437828 and -0.661437828.

Subproblem 1
x + 0.75 = 0.661437828

Simplifying
x + 0.75 = 0.661437828

Reorder the terms:
0.75 + x = 0.661437828

Solving
0.75 + x = 0.661437828

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 = 0.661437828 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = 0.661437828 + -0.75
x = 0.661437828 + -0.75

Combine like terms: 0.661437828 + -0.75 = -0.088562172
x = -0.088562172

Simplifying
x = -0.088562172

Subproblem 2
x + 0.75 = -0.661437828

Simplifying
x + 0.75 = -0.661437828

Reorder the terms:
0.75 + x = -0.661437828

Solving
0.75 + x = -0.661437828

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 = -0.661437828 + -0.75

Combine like terms: 0.75 + -0.75 = 0.00
0.00 + x = -0.661437828 + -0.75
x = -0.661437828 + -0.75

Combine like terms: -0.661437828 + -0.75 = -1.411437828
x = -1.411437828

Simplifying
x = -1.411437828

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.088562172, -1.411437828}
Solution
x = {-0.088562172, -1.411437828}