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

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

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

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

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

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

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

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

Combine like terms: 1x + -3x = -2x
12(-3 + -2x + x2) = 2
(-3 * 12 + -2x * 12 + x2 * 12) = 2
(-36 + -24x + 12x2) = 2

Solving
-36 + -24x + 12x2 = 2

Solving for variable 'x'.

Reorder the terms:
-36 + -2 + -24x + 12x2 = 2 + -2

Combine like terms: -36 + -2 = -38
-38 + -24x + 12x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-38 + -24x + 12x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-19 + -12x + 6x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-19 + -12x + 6x2)' equal to zero and attempt to solve:

Simplifying
-19 + -12x + 6x2 = 0

Solving
-19 + -12x + 6x2 = 0

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

Divide each side by '6'.
-3.166666667 + -2x + x2 = 0

Move the constant term to the right:

Add '3.166666667' to each side of the equation.
-3.166666667 + -2x + 3.166666667 + x2 = 0 + 3.166666667

Reorder the terms:
-3.166666667 + 3.166666667 + -2x + x2 = 0 + 3.166666667

Combine like terms: -3.166666667 + 3.166666667 = 0.000000000
0.000000000 + -2x + x2 = 0 + 3.166666667
-2x + x2 = 0 + 3.166666667

Combine like terms: 0 + 3.166666667 = 3.166666667
-2x + x2 = 3.166666667

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = 3.166666667 + 1

Reorder the terms:
1 + -2x + x2 = 3.166666667 + 1

Combine like terms: 3.166666667 + 1 = 4.166666667
1 + -2x + x2 = 4.166666667

Factor a perfect square on the left side:
(x + -1)(x + -1) = 4.166666667

Calculate the square root of the right side: 2.041241452

Break this problem into two subproblems by setting 
(x + -1) equal to 2.041241452 and -2.041241452.

Subproblem 1
x + -1 = 2.041241452

Simplifying
x + -1 = 2.041241452

Reorder the terms:
-1 + x = 2.041241452

Solving
-1 + x = 2.041241452

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = 2.041241452 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.041241452 + 1
x = 2.041241452 + 1

Combine like terms: 2.041241452 + 1 = 3.041241452
x = 3.041241452

Simplifying
x = 3.041241452

Subproblem 2
x + -1 = -2.041241452

Simplifying
x + -1 = -2.041241452

Reorder the terms:
-1 + x = -2.041241452

Solving
-1 + x = -2.041241452

Solving for variable 'x'.

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

Add '1' to each side of the equation.
-1 + 1 + x = -2.041241452 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.041241452 + 1
x = -2.041241452 + 1

Combine like terms: -2.041241452 + 1 = -1.041241452
x = -1.041241452

Simplifying
x = -1.041241452

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.041241452, -1.041241452}
Solution
x = {3.041241452, -1.041241452}