(x-1)(2x+6)=(x-2)(3x+2)

Solution for (x-1)(2x+6)=(x-2)(3x+2) equation:

Simplifying
(x + -1)(2x + 6) = (x + -2)(3x + 2)

Reorder the terms:
(-1 + x)(2x + 6) = (x + -2)(3x + 2)

Reorder the terms:
(-1 + x)(6 + 2x) = (x + -2)(3x + 2)

Multiply (-1 + x) * (6 + 2x)
(-1(6 + 2x) + x(6 + 2x)) = (x + -2)(3x + 2)
((6 * -1 + 2x * -1) + x(6 + 2x)) = (x + -2)(3x + 2)
((-6 + -2x) + x(6 + 2x)) = (x + -2)(3x + 2)
(-6 + -2x + (6 * x + 2x * x)) = (x + -2)(3x + 2)
(-6 + -2x + (6x + 2x2)) = (x + -2)(3x + 2)

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

Reorder the terms:
-6 + 4x + 2x2 = (-2 + x)(3x + 2)

Reorder the terms:
-6 + 4x + 2x2 = (-2 + x)(2 + 3x)

Multiply (-2 + x) * (2 + 3x)
-6 + 4x + 2x2 = (-2(2 + 3x) + x(2 + 3x))
-6 + 4x + 2x2 = ((2 * -2 + 3x * -2) + x(2 + 3x))
-6 + 4x + 2x2 = ((-4 + -6x) + x(2 + 3x))
-6 + 4x + 2x2 = (-4 + -6x + (2 * x + 3x * x))
-6 + 4x + 2x2 = (-4 + -6x + (2x + 3x2))

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

Solving
-6 + 4x + 2x2 = -4 + -4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-6 + 4 + 4x + 4x + 2x2 + -3x2 = -4 + -4x + 3x2 + 4 + 4x + -3x2

Combine like terms: -6 + 4 = -2
-2 + 4x + 4x + 2x2 + -3x2 = -4 + -4x + 3x2 + 4 + 4x + -3x2

Combine like terms: 4x + 4x = 8x
-2 + 8x + 2x2 + -3x2 = -4 + -4x + 3x2 + 4 + 4x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-2 + 8x + -1x2 = -4 + -4x + 3x2 + 4 + 4x + -3x2

Reorder the terms:
-2 + 8x + -1x2 = -4 + 4 + -4x + 4x + 3x2 + -3x2

Combine like terms: -4 + 4 = 0
-2 + 8x + -1x2 = 0 + -4x + 4x + 3x2 + -3x2
-2 + 8x + -1x2 = -4x + 4x + 3x2 + -3x2

Combine like terms: -4x + 4x = 0
-2 + 8x + -1x2 = 0 + 3x2 + -3x2
-2 + 8x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-2 + 8x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
2 + -8x + x2 = 0

Move the constant term to the right:

Add '-2' to each side of the equation.
2 + -8x + -2 + x2 = 0 + -2

Reorder the terms:
2 + -2 + -8x + x2 = 0 + -2

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

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

The x term is -8x.  Take half its coefficient (-4).
Square it (16) and add it to both sides.

Add '16' to each side of the equation.
-8x + 16 + x2 = -2 + 16

Reorder the terms:
16 + -8x + x2 = -2 + 16

Combine like terms: -2 + 16 = 14
16 + -8x + x2 = 14

Factor a perfect square on the left side:
(x + -4)(x + -4) = 14

Calculate the square root of the right side: 3.741657387

Break this problem into two subproblems by setting 
(x + -4) equal to 3.741657387 and -3.741657387.

Subproblem 1
x + -4 = 3.741657387

Simplifying
x + -4 = 3.741657387

Reorder the terms:
-4 + x = 3.741657387

Solving
-4 + x = 3.741657387

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = 3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + x = 3.741657387 + 4
x = 3.741657387 + 4

Combine like terms: 3.741657387 + 4 = 7.741657387
x = 7.741657387

Simplifying
x = 7.741657387

Subproblem 2
x + -4 = -3.741657387

Simplifying
x + -4 = -3.741657387

Reorder the terms:
-4 + x = -3.741657387

Solving
-4 + x = -3.741657387

Solving for variable 'x'.

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

Add '4' to each side of the equation.
-4 + 4 + x = -3.741657387 + 4

Combine like terms: -4 + 4 = 0
0 + x = -3.741657387 + 4
x = -3.741657387 + 4

Combine like terms: -3.741657387 + 4 = 0.258342613
x = 0.258342613

Simplifying
x = 0.258342613

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {7.741657387, 0.258342613}