3(4x-2)*(4x+3)=2

Solution for 3(4x-2)*(4x+3)=2 equation:

Simplifying
3(4x + -2)(4x + 3) = 2

Reorder the terms:
3(-2 + 4x)(4x + 3) = 2

Reorder the terms:
3(-2 + 4x)(3 + 4x) = 2

Multiply (-2 + 4x) * (3 + 4x)
3(-2(3 + 4x) + 4x * (3 + 4x)) = 2
3((3 * -2 + 4x * -2) + 4x * (3 + 4x)) = 2
3((-6 + -8x) + 4x * (3 + 4x)) = 2
3(-6 + -8x + (3 * 4x + 4x * 4x)) = 2
3(-6 + -8x + (12x + 16x2)) = 2

Combine like terms: -8x + 12x = 4x
3(-6 + 4x + 16x2) = 2
(-6 * 3 + 4x * 3 + 16x2 * 3) = 2
(-18 + 12x + 48x2) = 2

Solving
-18 + 12x + 48x2 = 2

Solving for variable 'x'.

Reorder the terms:
-18 + -2 + 12x + 48x2 = 2 + -2

Combine like terms: -18 + -2 = -20
-20 + 12x + 48x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-20 + 12x + 48x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(-5 + 3x + 12x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-5 + 3x + 12x2)' equal to zero and attempt to solve:

Simplifying
-5 + 3x + 12x2 = 0

Solving
-5 + 3x + 12x2 = 0

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

Divide each side by '12'.
-0.4166666667 + 0.25x + x2 = 0

Move the constant term to the right:

Add '0.4166666667' to each side of the equation.
-0.4166666667 + 0.25x + 0.4166666667 + x2 = 0 + 0.4166666667

Reorder the terms:
-0.4166666667 + 0.4166666667 + 0.25x + x2 = 0 + 0.4166666667

Combine like terms: -0.4166666667 + 0.4166666667 = 0.0000000000
0.0000000000 + 0.25x + x2 = 0 + 0.4166666667
0.25x + x2 = 0 + 0.4166666667

Combine like terms: 0 + 0.4166666667 = 0.4166666667
0.25x + x2 = 0.4166666667

The x term is 0.25x.  Take half its coefficient (0.125).
Square it (0.015625) and add it to both sides.

Add '0.015625' to each side of the equation.
0.25x + 0.015625 + x2 = 0.4166666667 + 0.015625

Reorder the terms:
0.015625 + 0.25x + x2 = 0.4166666667 + 0.015625

Combine like terms: 0.4166666667 + 0.015625 = 0.4322916667
0.015625 + 0.25x + x2 = 0.4322916667

Factor a perfect square on the left side:
(x + 0.125)(x + 0.125) = 0.4322916667

Calculate the square root of the right side: 0.65748891

Break this problem into two subproblems by setting 
(x + 0.125) equal to 0.65748891 and -0.65748891.

Subproblem 1
x + 0.125 = 0.65748891

Simplifying
x + 0.125 = 0.65748891

Reorder the terms:
0.125 + x = 0.65748891

Solving
0.125 + x = 0.65748891

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = 0.65748891 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = 0.65748891 + -0.125
x = 0.65748891 + -0.125

Combine like terms: 0.65748891 + -0.125 = 0.53248891
x = 0.53248891

Simplifying
x = 0.53248891

Subproblem 2
x + 0.125 = -0.65748891

Simplifying
x + 0.125 = -0.65748891

Reorder the terms:
0.125 + x = -0.65748891

Solving
0.125 + x = -0.65748891

Solving for variable 'x'.

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

Add '-0.125' to each side of the equation.
0.125 + -0.125 + x = -0.65748891 + -0.125

Combine like terms: 0.125 + -0.125 = 0.000
0.000 + x = -0.65748891 + -0.125
x = -0.65748891 + -0.125

Combine like terms: -0.65748891 + -0.125 = -0.78248891
x = -0.78248891

Simplifying
x = -0.78248891

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.53248891, -0.78248891}
Solution
x = {0.53248891, -0.78248891}