(x+5)(2x-1)=4x

Solution for (x+5)(2x-1)=4x equation:

Simplifying
(x + 5)(2x + -1) = 4x

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

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

Multiply (5 + x) * (-1 + 2x)
(5(-1 + 2x) + x(-1 + 2x)) = 4x
((-1 * 5 + 2x * 5) + x(-1 + 2x)) = 4x
((-5 + 10x) + x(-1 + 2x)) = 4x
(-5 + 10x + (-1 * x + 2x * x)) = 4x
(-5 + 10x + (-1x + 2x2)) = 4x

Combine like terms: 10x + -1x = 9x
(-5 + 9x + 2x2) = 4x

Solving
-5 + 9x + 2x2 = 4x

Solving for variable 'x'.

Reorder the terms:
-5 + 9x + -4x + 2x2 = 4x + -4x

Combine like terms: 9x + -4x = 5x
-5 + 5x + 2x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-5 + 5x + 2x2 = 0

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

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

Move the constant term to the right:

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

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

Combine like terms: -2.5 + 2.5 = 0.0
0.0 + 2.5x + x2 = 0 + 2.5
2.5x + x2 = 0 + 2.5

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

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 = 2.5 + 1.5625

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

Combine like terms: 2.5 + 1.5625 = 4.0625
1.5625 + 2.5x + x2 = 4.0625

Factor a perfect square on the left side:
(x + 1.25)(x + 1.25) = 4.0625

Calculate the square root of the right side: 2.015564437

Break this problem into two subproblems by setting 
(x + 1.25) equal to 2.015564437 and -2.015564437.

Subproblem 1
x + 1.25 = 2.015564437

Simplifying
x + 1.25 = 2.015564437

Reorder the terms:
1.25 + x = 2.015564437

Solving
1.25 + x = 2.015564437

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 = 2.015564437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = 2.015564437 + -1.25
x = 2.015564437 + -1.25

Combine like terms: 2.015564437 + -1.25 = 0.765564437
x = 0.765564437

Simplifying
x = 0.765564437

Subproblem 2
x + 1.25 = -2.015564437

Simplifying
x + 1.25 = -2.015564437

Reorder the terms:
1.25 + x = -2.015564437

Solving
1.25 + x = -2.015564437

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 = -2.015564437 + -1.25

Combine like terms: 1.25 + -1.25 = 0.00
0.00 + x = -2.015564437 + -1.25
x = -2.015564437 + -1.25

Combine like terms: -2.015564437 + -1.25 = -3.265564437
x = -3.265564437

Simplifying
x = -3.265564437

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {0.765564437, -3.265564437}