(4x+1)(-2x+2)=12x-6(3x+4)

Solution for (4x+1)(-2x+2)=12x-6(3x+4) equation:

Simplifying
(4x + 1)(-2x + 2) = 12x + -6(3x + 4)

Reorder the terms:
(1 + 4x)(-2x + 2) = 12x + -6(3x + 4)

Reorder the terms:
(1 + 4x)(2 + -2x) = 12x + -6(3x + 4)

Multiply (1 + 4x) * (2 + -2x)
(1(2 + -2x) + 4x * (2 + -2x)) = 12x + -6(3x + 4)
((2 * 1 + -2x * 1) + 4x * (2 + -2x)) = 12x + -6(3x + 4)
((2 + -2x) + 4x * (2 + -2x)) = 12x + -6(3x + 4)
(2 + -2x + (2 * 4x + -2x * 4x)) = 12x + -6(3x + 4)
(2 + -2x + (8x + -8x2)) = 12x + -6(3x + 4)

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

Reorder the terms:
2 + 6x + -8x2 = 12x + -6(4 + 3x)
2 + 6x + -8x2 = 12x + (4 * -6 + 3x * -6)
2 + 6x + -8x2 = 12x + (-24 + -18x)

Reorder the terms:
2 + 6x + -8x2 = -24 + 12x + -18x

Combine like terms: 12x + -18x = -6x
2 + 6x + -8x2 = -24 + -6x

Solving
2 + 6x + -8x2 = -24 + -6x

Solving for variable 'x'.

Reorder the terms:
2 + 24 + 6x + 6x + -8x2 = -24 + -6x + 24 + 6x

Combine like terms: 2 + 24 = 26
26 + 6x + 6x + -8x2 = -24 + -6x + 24 + 6x

Combine like terms: 6x + 6x = 12x
26 + 12x + -8x2 = -24 + -6x + 24 + 6x

Reorder the terms:
26 + 12x + -8x2 = -24 + 24 + -6x + 6x

Combine like terms: -24 + 24 = 0
26 + 12x + -8x2 = 0 + -6x + 6x
26 + 12x + -8x2 = -6x + 6x

Combine like terms: -6x + 6x = 0
26 + 12x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(13 + 6x + -4x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(13 + 6x + -4x2)' equal to zero and attempt to solve:

Simplifying
13 + 6x + -4x2 = 0

Solving
13 + 6x + -4x2 = 0

Begin completing the square.  Divide all terms by
-4 the coefficient of the squared term: 

Divide each side by '-4'.
-3.25 + -1.5x + x2 = 0

Move the constant term to the right:

Add '3.25' to each side of the equation.
-3.25 + -1.5x + 3.25 + x2 = 0 + 3.25

Reorder the terms:
-3.25 + 3.25 + -1.5x + x2 = 0 + 3.25

Combine like terms: -3.25 + 3.25 = 0.00
0.00 + -1.5x + x2 = 0 + 3.25
-1.5x + x2 = 0 + 3.25

Combine like terms: 0 + 3.25 = 3.25
-1.5x + x2 = 3.25

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 = 3.25 + 0.5625

Reorder the terms:
0.5625 + -1.5x + x2 = 3.25 + 0.5625

Combine like terms: 3.25 + 0.5625 = 3.8125
0.5625 + -1.5x + x2 = 3.8125

Factor a perfect square on the left side:
(x + -0.75)(x + -0.75) = 3.8125

Calculate the square root of the right side: 1.952562419

Break this problem into two subproblems by setting 
(x + -0.75) equal to 1.952562419 and -1.952562419.

Subproblem 1
x + -0.75 = 1.952562419

Simplifying
x + -0.75 = 1.952562419

Reorder the terms:
-0.75 + x = 1.952562419

Solving
-0.75 + x = 1.952562419

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 = 1.952562419 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = 1.952562419 + 0.75
x = 1.952562419 + 0.75

Combine like terms: 1.952562419 + 0.75 = 2.702562419
x = 2.702562419

Simplifying
x = 2.702562419

Subproblem 2
x + -0.75 = -1.952562419

Simplifying
x + -0.75 = -1.952562419

Reorder the terms:
-0.75 + x = -1.952562419

Solving
-0.75 + x = -1.952562419

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 = -1.952562419 + 0.75

Combine like terms: -0.75 + 0.75 = 0.00
0.00 + x = -1.952562419 + 0.75
x = -1.952562419 + 0.75

Combine like terms: -1.952562419 + 0.75 = -1.202562419
x = -1.202562419

Simplifying
x = -1.202562419

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {2.702562419, -1.202562419}
Solution
x = {2.702562419, -1.202562419}