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

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

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

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

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

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

Combine like terms: -12x + 4x = -8x
(-6 + -8x + 8x2) = 3

Solving
-6 + -8x + 8x2 = 3

Solving for variable 'x'.

Reorder the terms:
-6 + -3 + -8x + 8x2 = 3 + -3

Combine like terms: -6 + -3 = -9
-9 + -8x + 8x2 = 3 + -3

Combine like terms: 3 + -3 = 0
-9 + -8x + 8x2 = 0

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

Divide each side by '8'.
-1.125 + -1x + x2 = 0

Move the constant term to the right:

Add '1.125' to each side of the equation.
-1.125 + -1x + 1.125 + x2 = 0 + 1.125

Reorder the terms:
-1.125 + 1.125 + -1x + x2 = 0 + 1.125

Combine like terms: -1.125 + 1.125 = 0.000
0.000 + -1x + x2 = 0 + 1.125
-1x + x2 = 0 + 1.125

Combine like terms: 0 + 1.125 = 1.125
-1x + x2 = 1.125

The x term is -1x.  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.
-1x + 0.25 + x2 = 1.125 + 0.25

Reorder the terms:
0.25 + -1x + x2 = 1.125 + 0.25

Combine like terms: 1.125 + 0.25 = 1.375
0.25 + -1x + x2 = 1.375

Factor a perfect square on the left side:
(x + -0.5)(x + -0.5) = 1.375

Calculate the square root of the right side: 1.17260394

Break this problem into two subproblems by setting 
(x + -0.5) equal to 1.17260394 and -1.17260394.

Subproblem 1
x + -0.5 = 1.17260394

Simplifying
x + -0.5 = 1.17260394

Reorder the terms:
-0.5 + x = 1.17260394

Solving
-0.5 + x = 1.17260394

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 = 1.17260394 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = 1.17260394 + 0.5
x = 1.17260394 + 0.5

Combine like terms: 1.17260394 + 0.5 = 1.67260394
x = 1.67260394

Simplifying
x = 1.67260394

Subproblem 2
x + -0.5 = -1.17260394

Simplifying
x + -0.5 = -1.17260394

Reorder the terms:
-0.5 + x = -1.17260394

Solving
-0.5 + x = -1.17260394

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 = -1.17260394 + 0.5

Combine like terms: -0.5 + 0.5 = 0.0
0.0 + x = -1.17260394 + 0.5
x = -1.17260394 + 0.5

Combine like terms: -1.17260394 + 0.5 = -0.67260394
x = -0.67260394

Simplifying
x = -0.67260394

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.67260394, -0.67260394}