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

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

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

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

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

Multiply (3 + 2x) * (-1 + x)
(3(-1 + x) + 2x * (-1 + x)) = 66
((-1 * 3 + x * 3) + 2x * (-1 + x)) = 66
((-3 + 3x) + 2x * (-1 + x)) = 66
(-3 + 3x + (-1 * 2x + x * 2x)) = 66
(-3 + 3x + (-2x + 2x2)) = 66

Combine like terms: 3x + -2x = 1x
(-3 + 1x + 2x2) = 66

Solving
-3 + 1x + 2x2 = 66

Solving for variable 'x'.

Reorder the terms:
-3 + -66 + 1x + 2x2 = 66 + -66

Combine like terms: -3 + -66 = -69
-69 + 1x + 2x2 = 66 + -66

Combine like terms: 66 + -66 = 0
-69 + 1x + 2x2 = 0

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

Divide each side by '2'.
-34.5 + 0.5x + x2 = 0

Move the constant term to the right:

Add '34.5' to each side of the equation.
-34.5 + 0.5x + 34.5 + x2 = 0 + 34.5

Reorder the terms:
-34.5 + 34.5 + 0.5x + x2 = 0 + 34.5

Combine like terms: -34.5 + 34.5 = 0.0
0.0 + 0.5x + x2 = 0 + 34.5
0.5x + x2 = 0 + 34.5

Combine like terms: 0 + 34.5 = 34.5
0.5x + x2 = 34.5

The x term is 0.5x.  Take half its coefficient (0.25).
Square it (0.0625) and add it to both sides.

Add '0.0625' to each side of the equation.
0.5x + 0.0625 + x2 = 34.5 + 0.0625

Reorder the terms:
0.0625 + 0.5x + x2 = 34.5 + 0.0625

Combine like terms: 34.5 + 0.0625 = 34.5625
0.0625 + 0.5x + x2 = 34.5625

Factor a perfect square on the left side:
(x + 0.25)(x + 0.25) = 34.5625

Calculate the square root of the right side: 5.878988008

Break this problem into two subproblems by setting 
(x + 0.25) equal to 5.878988008 and -5.878988008.

Subproblem 1
x + 0.25 = 5.878988008

Simplifying
x + 0.25 = 5.878988008

Reorder the terms:
0.25 + x = 5.878988008

Solving
0.25 + x = 5.878988008

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = 5.878988008 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = 5.878988008 + -0.25
x = 5.878988008 + -0.25

Combine like terms: 5.878988008 + -0.25 = 5.628988008
x = 5.628988008

Simplifying
x = 5.628988008

Subproblem 2
x + 0.25 = -5.878988008

Simplifying
x + 0.25 = -5.878988008

Reorder the terms:
0.25 + x = -5.878988008

Solving
0.25 + x = -5.878988008

Solving for variable 'x'.

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

Add '-0.25' to each side of the equation.
0.25 + -0.25 + x = -5.878988008 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + x = -5.878988008 + -0.25
x = -5.878988008 + -0.25

Combine like terms: -5.878988008 + -0.25 = -6.128988008
x = -6.128988008

Simplifying
x = -6.128988008

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.628988008, -6.128988008}