((x+3)*2)(x-1)=66

Solution for ((x+3)*2)(x-1)=66 equation:

Simplifying
((x + 3) * 2)(x + -1) = 66

Reorder the terms:
((3 + x) * 2)(x + -1) = 66

Reorder the terms for easier multiplication:
(2(3 + x))(x + -1) = 66
((3 * 2 + x * 2))(x + -1) = 66
((6 + 2x))(x + -1) = 66

Reorder the terms:
(6 + 2x)(-1 + x) = 66

Multiply (6 + 2x) * (-1 + x)
(6(-1 + x) + 2x * (-1 + x)) = 66
((-1 * 6 + x * 6) + 2x * (-1 + x)) = 66
((-6 + 6x) + 2x * (-1 + x)) = 66
(-6 + 6x + (-1 * 2x + x * 2x)) = 66
(-6 + 6x + (-2x + 2x2)) = 66

Combine like terms: 6x + -2x = 4x
(-6 + 4x + 2x2) = 66

Solving
-6 + 4x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
-6 + -66 + 4x + 2x2 = 66 + -66

Combine like terms: -6 + -66 = -72
-72 + 4x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-72 + 4x + 2x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(-36 + 2x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-36 + 2x + x2)' equal to zero and attempt to solve:

Simplifying
-36 + 2x + x2 = 0

Solving
-36 + 2x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '36' to each side of the equation.
-36 + 2x + 36 + x2 = 0 + 36

Reorder the terms:
-36 + 36 + 2x + x2 = 0 + 36

Combine like terms: -36 + 36 = 0
0 + 2x + x2 = 0 + 36
2x + x2 = 0 + 36

Combine like terms: 0 + 36 = 36
2x + x2 = 36

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 = 36 + 1

Reorder the terms:
1 + 2x + x2 = 36 + 1

Combine like terms: 36 + 1 = 37
1 + 2x + x2 = 37

Factor a perfect square on the left side:
(x + 1)(x + 1) = 37

Calculate the square root of the right side: 6.08276253

Break this problem into two subproblems by setting 
(x + 1) equal to 6.08276253 and -6.08276253.

Subproblem 1
x + 1 = 6.08276253

Simplifying
x + 1 = 6.08276253

Reorder the terms:
1 + x = 6.08276253

Solving
1 + x = 6.08276253

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 = 6.08276253 + -1

Combine like terms: 1 + -1 = 0
0 + x = 6.08276253 + -1
x = 6.08276253 + -1

Combine like terms: 6.08276253 + -1 = 5.08276253
x = 5.08276253

Simplifying
x = 5.08276253

Subproblem 2
x + 1 = -6.08276253

Simplifying
x + 1 = -6.08276253

Reorder the terms:
1 + x = -6.08276253

Solving
1 + x = -6.08276253

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 = -6.08276253 + -1

Combine like terms: 1 + -1 = 0
0 + x = -6.08276253 + -1
x = -6.08276253 + -1

Combine like terms: -6.08276253 + -1 = -7.08276253
x = -7.08276253

Simplifying
x = -7.08276253

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.08276253, -7.08276253}
Solution
x = {5.08276253, -7.08276253}