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

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

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

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

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

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

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

Solving
-4 + -7x + 2x2 = x

Solving for variable 'x'.

Reorder the terms:
-4 + -7x + -1x + 2x2 = x + -1x

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

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

Factor out the Greatest Common Factor (GCF), '2'.
2(-2 + -4x + x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-2 + -4x + x2)' equal to zero and attempt to solve:

Simplifying
-2 + -4x + x2 = 0

Solving
-2 + -4x + x2 = 0

Begin completing the square.

Move the constant term to the right:

Add '2' to each side of the equation.
-2 + -4x + 2 + x2 = 0 + 2

Reorder the terms:
-2 + 2 + -4x + x2 = 0 + 2

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

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

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = 2 + 4

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

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

Factor a perfect square on the left side:
(x + -2)(x + -2) = 6

Calculate the square root of the right side: 2.449489743

Break this problem into two subproblems by setting 
(x + -2) equal to 2.449489743 and -2.449489743.

Subproblem 1
x + -2 = 2.449489743

Simplifying
x + -2 = 2.449489743

Reorder the terms:
-2 + x = 2.449489743

Solving
-2 + x = 2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = 2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.449489743 + 2
x = 2.449489743 + 2

Combine like terms: 2.449489743 + 2 = 4.449489743
x = 4.449489743

Simplifying
x = 4.449489743

Subproblem 2
x + -2 = -2.449489743

Simplifying
x + -2 = -2.449489743

Reorder the terms:
-2 + x = -2.449489743

Solving
-2 + x = -2.449489743

Solving for variable 'x'.

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

Add '2' to each side of the equation.
-2 + 2 + x = -2.449489743 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.449489743 + 2
x = -2.449489743 + 2

Combine like terms: -2.449489743 + 2 = -0.449489743
x = -0.449489743

Simplifying
x = -0.449489743

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.449489743, -0.449489743}
Solution
x = {4.449489743, -0.449489743}