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

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

Simplifying
3(4x + -1) * 2(x + 2) = 2(x + 1)

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

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

Reorder the terms for easier multiplication:
3 * 2(-1 + 4x)(2 + x) = 2(x + 1)

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

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

Combine like terms: -1x + 8x = 7x
6(-2 + 7x + 4x2) = 2(x + 1)
(-2 * 6 + 7x * 6 + 4x2 * 6) = 2(x + 1)
(-12 + 42x + 24x2) = 2(x + 1)

Reorder the terms:
-12 + 42x + 24x2 = 2(1 + x)
-12 + 42x + 24x2 = (1 * 2 + x * 2)
-12 + 42x + 24x2 = (2 + 2x)

Solving
-12 + 42x + 24x2 = 2 + 2x

Solving for variable 'x'.

Reorder the terms:
-12 + -2 + 42x + -2x + 24x2 = 2 + 2x + -2 + -2x

Combine like terms: -12 + -2 = -14
-14 + 42x + -2x + 24x2 = 2 + 2x + -2 + -2x

Combine like terms: 42x + -2x = 40x
-14 + 40x + 24x2 = 2 + 2x + -2 + -2x

Reorder the terms:
-14 + 40x + 24x2 = 2 + -2 + 2x + -2x

Combine like terms: 2 + -2 = 0
-14 + 40x + 24x2 = 0 + 2x + -2x
-14 + 40x + 24x2 = 2x + -2x

Combine like terms: 2x + -2x = 0
-14 + 40x + 24x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-7 + 20x + 12x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-7 + 20x + 12x2)' equal to zero and attempt to solve:

Simplifying
-7 + 20x + 12x2 = 0

Solving
-7 + 20x + 12x2 = 0

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

Divide each side by '12'.
-0.5833333333 + 1.666666667x + x2 = 0

Move the constant term to the right:

Add '0.5833333333' to each side of the equation.
-0.5833333333 + 1.666666667x + 0.5833333333 + x2 = 0 + 0.5833333333

Reorder the terms:
-0.5833333333 + 0.5833333333 + 1.666666667x + x2 = 0 + 0.5833333333

Combine like terms: -0.5833333333 + 0.5833333333 = 0.0000000000
0.0000000000 + 1.666666667x + x2 = 0 + 0.5833333333
1.666666667x + x2 = 0 + 0.5833333333

Combine like terms: 0 + 0.5833333333 = 0.5833333333
1.666666667x + x2 = 0.5833333333

The x term is 1.666666667x.  Take half its coefficient (0.8333333335).
Square it (0.6944444447) and add it to both sides.

Add '0.6944444447' to each side of the equation.
1.666666667x + 0.6944444447 + x2 = 0.5833333333 + 0.6944444447

Reorder the terms:
0.6944444447 + 1.666666667x + x2 = 0.5833333333 + 0.6944444447

Combine like terms: 0.5833333333 + 0.6944444447 = 1.277777778
0.6944444447 + 1.666666667x + x2 = 1.277777778

Factor a perfect square on the left side:
(x + 0.8333333335)(x + 0.8333333335) = 1.277777778

Calculate the square root of the right side: 1.130388331

Break this problem into two subproblems by setting 
(x + 0.8333333335) equal to 1.130388331 and -1.130388331.

Subproblem 1
x + 0.8333333335 = 1.130388331

Simplifying
x + 0.8333333335 = 1.130388331

Reorder the terms:
0.8333333335 + x = 1.130388331

Solving
0.8333333335 + x = 1.130388331

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = 1.130388331 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = 1.130388331 + -0.8333333335
x = 1.130388331 + -0.8333333335

Combine like terms: 1.130388331 + -0.8333333335 = 0.2970549975
x = 0.2970549975

Simplifying
x = 0.2970549975

Subproblem 2
x + 0.8333333335 = -1.130388331

Simplifying
x + 0.8333333335 = -1.130388331

Reorder the terms:
0.8333333335 + x = -1.130388331

Solving
0.8333333335 + x = -1.130388331

Solving for variable 'x'.

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

Add '-0.8333333335' to each side of the equation.
0.8333333335 + -0.8333333335 + x = -1.130388331 + -0.8333333335

Combine like terms: 0.8333333335 + -0.8333333335 = 0.0000000000
0.0000000000 + x = -1.130388331 + -0.8333333335
x = -1.130388331 + -0.8333333335

Combine like terms: -1.130388331 + -0.8333333335 = -1.9637216645
x = -1.9637216645

Simplifying
x = -1.9637216645

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.2970549975, -1.9637216645}
Solution
x = {0.2970549975, -1.9637216645}