(2x+1)(x-4)+(x-2)=3x(x+2)

Solution for (2x+1)(x-4)+(x-2)=3x(x+2) equation:

Simplifying
(2x + 1)(x + -4) + (x + -2) = 3x(x + 2)

Reorder the terms:
(1 + 2x)(x + -4) + (x + -2) = 3x(x + 2)

Reorder the terms:
(1 + 2x)(-4 + x) + (x + -2) = 3x(x + 2)

Multiply (1 + 2x) * (-4 + x)
(1(-4 + x) + 2x * (-4 + x)) + (x + -2) = 3x(x + 2)
((-4 * 1 + x * 1) + 2x * (-4 + x)) + (x + -2) = 3x(x + 2)
((-4 + 1x) + 2x * (-4 + x)) + (x + -2) = 3x(x + 2)
(-4 + 1x + (-4 * 2x + x * 2x)) + (x + -2) = 3x(x + 2)
(-4 + 1x + (-8x + 2x2)) + (x + -2) = 3x(x + 2)

Combine like terms: 1x + -8x = -7x
(-4 + -7x + 2x2) + (x + -2) = 3x(x + 2)

Reorder the terms:
-4 + -7x + 2x2 + (-2 + x) = 3x(x + 2)

Remove parenthesis around (-2 + x)
-4 + -7x + 2x2 + -2 + x = 3x(x + 2)

Reorder the terms:
-4 + -2 + -7x + x + 2x2 = 3x(x + 2)

Combine like terms: -4 + -2 = -6
-6 + -7x + x + 2x2 = 3x(x + 2)

Combine like terms: -7x + x = -6x
-6 + -6x + 2x2 = 3x(x + 2)

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

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

Solving for variable 'x'.

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

Combine like terms: -6x + -6x = -12x
-6 + -12x + 2x2 + -3x2 = 6x + 3x2 + -6x + -3x2

Combine like terms: 2x2 + -3x2 = -1x2
-6 + -12x + -1x2 = 6x + 3x2 + -6x + -3x2

Reorder the terms:
-6 + -12x + -1x2 = 6x + -6x + 3x2 + -3x2

Combine like terms: 6x + -6x = 0
-6 + -12x + -1x2 = 0 + 3x2 + -3x2
-6 + -12x + -1x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-6 + -12x + -1x2 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(6 + 12x + x2) = 0

Ignore the factor -1.
Subproblem 1
Set the factor '(6 + 12x + x2)' equal to zero and attempt to solve:

Simplifying
6 + 12x + x2 = 0

Solving
6 + 12x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '-6' to each side of the equation.
6 + 12x + -6 + x2 = 0 + -6

Reorder the terms:
6 + -6 + 12x + x2 = 0 + -6

Combine like terms: 6 + -6 = 0
0 + 12x + x2 = 0 + -6
12x + x2 = 0 + -6

Combine like terms: 0 + -6 = -6
12x + x2 = -6

The x term is 12x.  Take half its coefficient (6).
Square it (36) and add it to both sides.

Add '36' to each side of the equation.
12x + 36 + x2 = -6 + 36

Reorder the terms:
36 + 12x + x2 = -6 + 36

Combine like terms: -6 + 36 = 30
36 + 12x + x2 = 30

Factor a perfect square on the left side:
(x + 6)(x + 6) = 30

Calculate the square root of the right side: 5.477225575

Break this problem into two subproblems by setting 
(x + 6) equal to 5.477225575 and -5.477225575.

Subproblem 1
x + 6 = 5.477225575

Simplifying
x + 6 = 5.477225575

Reorder the terms:
6 + x = 5.477225575

Solving
6 + x = 5.477225575

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = 5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + x = 5.477225575 + -6
x = 5.477225575 + -6

Combine like terms: 5.477225575 + -6 = -0.522774425
x = -0.522774425

Simplifying
x = -0.522774425

Subproblem 2
x + 6 = -5.477225575

Simplifying
x + 6 = -5.477225575

Reorder the terms:
6 + x = -5.477225575

Solving
6 + x = -5.477225575

Solving for variable 'x'.

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

Add '-6' to each side of the equation.
6 + -6 + x = -5.477225575 + -6

Combine like terms: 6 + -6 = 0
0 + x = -5.477225575 + -6
x = -5.477225575 + -6

Combine like terms: -5.477225575 + -6 = -11.477225575
x = -11.477225575

Simplifying
x = -11.477225575

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {-0.522774425, -11.477225575}
Solution
x = {-0.522774425, -11.477225575}