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

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

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

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

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

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

Combine like terms: -3x + 1x = -2x
2(-3 + -2x + x2) = 2
(-3 * 2 + -2x * 2 + x2 * 2) = 2
(-6 + -4x + 2x2) = 2

Solving
-6 + -4x + 2x2 = 2

Solving for variable 'x'.

Reorder the terms:
-6 + -2 + -4x + 2x2 = 2 + -2

Combine like terms: -6 + -2 = -8
-8 + -4x + 2x2 = 2 + -2

Combine like terms: 2 + -2 = 0
-8 + -4x + 2x2 = 0

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

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

Simplifying
-4 + -2x + x2 = 0

Solving
-4 + -2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2x + x2 = 0 + 4
-2x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2x + x2 = 4

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 = 4 + 1

Reorder the terms:
1 + -2x + x2 = 4 + 1

Combine like terms: 4 + 1 = 5
1 + -2x + x2 = 5

Factor a perfect square on the left side:
(x + -1)(x + -1) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -1) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -1 = 2.236067978

Simplifying
x + -1 = 2.236067978

Reorder the terms:
-1 + x = 2.236067978

Solving
-1 + x = 2.236067978

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 = 2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = 2.236067978 + 1
x = 2.236067978 + 1

Combine like terms: 2.236067978 + 1 = 3.236067978
x = 3.236067978

Simplifying
x = 3.236067978

Subproblem 2
x + -1 = -2.236067978

Simplifying
x + -1 = -2.236067978

Reorder the terms:
-1 + x = -2.236067978

Solving
-1 + x = -2.236067978

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 = -2.236067978 + 1

Combine like terms: -1 + 1 = 0
0 + x = -2.236067978 + 1
x = -2.236067978 + 1

Combine like terms: -2.236067978 + 1 = -1.236067978
x = -1.236067978

Simplifying
x = -1.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.236067978, -1.236067978}
Solution
x = {3.236067978, -1.236067978}