(2x+2)(x-1)=5x+6

Solution for (2x+2)(x-1)=5x+6 equation:

Simplifying
(2x + 2)(x + -1) = 5x + 6

Reorder the terms:
(2 + 2x)(x + -1) = 5x + 6

Reorder the terms:
(2 + 2x)(-1 + x) = 5x + 6

Multiply (2 + 2x) * (-1 + x)
(2(-1 + x) + 2x * (-1 + x)) = 5x + 6
((-1 * 2 + x * 2) + 2x * (-1 + x)) = 5x + 6
((-2 + 2x) + 2x * (-1 + x)) = 5x + 6
(-2 + 2x + (-1 * 2x + x * 2x)) = 5x + 6
(-2 + 2x + (-2x + 2x2)) = 5x + 6

Combine like terms: 2x + -2x = 0
(-2 + 0 + 2x2) = 5x + 6
(-2 + 2x2) = 5x + 6

Reorder the terms:
-2 + 2x2 = 6 + 5x

Solving
-2 + 2x2 = 6 + 5x

Solving for variable 'x'.

Reorder the terms:
-2 + -6 + -5x + 2x2 = 6 + 5x + -6 + -5x

Combine like terms: -2 + -6 = -8
-8 + -5x + 2x2 = 6 + 5x + -6 + -5x

Reorder the terms:
-8 + -5x + 2x2 = 6 + -6 + 5x + -5x

Combine like terms: 6 + -6 = 0
-8 + -5x + 2x2 = 0 + 5x + -5x
-8 + -5x + 2x2 = 5x + -5x

Combine like terms: 5x + -5x = 0
-8 + -5x + 2x2 = 0

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

Divide each side by '2'.
-4 + -2.5x + x2 = 0

Move the constant term to the right:

Add '4' to each side of the equation.
-4 + -2.5x + 4 + x2 = 0 + 4

Reorder the terms:
-4 + 4 + -2.5x + x2 = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -2.5x + x2 = 0 + 4
-2.5x + x2 = 0 + 4

Combine like terms: 0 + 4 = 4
-2.5x + x2 = 4

The x term is -2.5x.  Take half its coefficient (-1.25).
Square it (1.5625) and add it to both sides.

Add '1.5625' to each side of the equation.
-2.5x + 1.5625 + x2 = 4 + 1.5625

Reorder the terms:
1.5625 + -2.5x + x2 = 4 + 1.5625

Combine like terms: 4 + 1.5625 = 5.5625
1.5625 + -2.5x + x2 = 5.5625

Factor a perfect square on the left side:
(x + -1.25)(x + -1.25) = 5.5625

Calculate the square root of the right side: 2.358495283

Break this problem into two subproblems by setting 
(x + -1.25) equal to 2.358495283 and -2.358495283.

Subproblem 1
x + -1.25 = 2.358495283

Simplifying
x + -1.25 = 2.358495283

Reorder the terms:
-1.25 + x = 2.358495283

Solving
-1.25 + x = 2.358495283

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = 2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = 2.358495283 + 1.25
x = 2.358495283 + 1.25

Combine like terms: 2.358495283 + 1.25 = 3.608495283
x = 3.608495283

Simplifying
x = 3.608495283

Subproblem 2
x + -1.25 = -2.358495283

Simplifying
x + -1.25 = -2.358495283

Reorder the terms:
-1.25 + x = -2.358495283

Solving
-1.25 + x = -2.358495283

Solving for variable 'x'.

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

Add '1.25' to each side of the equation.
-1.25 + 1.25 + x = -2.358495283 + 1.25

Combine like terms: -1.25 + 1.25 = 0.00
0.00 + x = -2.358495283 + 1.25
x = -2.358495283 + 1.25

Combine like terms: -2.358495283 + 1.25 = -1.108495283
x = -1.108495283

Simplifying
x = -1.108495283

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.608495283, -1.108495283}