6x+4=2x(2x-5)

Solution for 6x+4=2x(2x-5) equation:

Simplifying
6x + 4 = 2x(2x + -5)

Reorder the terms:
4 + 6x = 2x(2x + -5)

Reorder the terms:
4 + 6x = 2x(-5 + 2x)
4 + 6x = (-5 * 2x + 2x * 2x)
4 + 6x = (-10x + 4x2)

Solving
4 + 6x = -10x + 4x2

Solving for variable 'x'.

Combine like terms: 6x + 10x = 16x
4 + 16x + -4x2 = -10x + 4x2 + 10x + -4x2

Reorder the terms:
4 + 16x + -4x2 = -10x + 10x + 4x2 + -4x2

Combine like terms: -10x + 10x = 0
4 + 16x + -4x2 = 0 + 4x2 + -4x2
4 + 16x + -4x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
4 + 16x + -4x2 = 0

Factor out the Greatest Common Factor (GCF), '4'.
4(1 + 4x + -1x2) = 0

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

Simplifying
1 + 4x + -1x2 = 0

Solving
1 + 4x + -1x2 = 0

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

Divide each side by '-1'.
-1 + -4x + x2 = 0

Move the constant term to the right:

Add '1' to each side of the equation.
-1 + -4x + 1 + x2 = 0 + 1

Reorder the terms:
-1 + 1 + -4x + x2 = 0 + 1

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

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

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 = 1 + 4

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

Combine like terms: 1 + 4 = 5
4 + -4x + x2 = 5

Factor a perfect square on the left side:
(x + -2)(x + -2) = 5

Calculate the square root of the right side: 2.236067978

Break this problem into two subproblems by setting 
(x + -2) equal to 2.236067978 and -2.236067978.

Subproblem 1
x + -2 = 2.236067978

Simplifying
x + -2 = 2.236067978

Reorder the terms:
-2 + x = 2.236067978

Solving
-2 + x = 2.236067978

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 = 2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = 2.236067978 + 2
x = 2.236067978 + 2

Combine like terms: 2.236067978 + 2 = 4.236067978
x = 4.236067978

Simplifying
x = 4.236067978

Subproblem 2
x + -2 = -2.236067978

Simplifying
x + -2 = -2.236067978

Reorder the terms:
-2 + x = -2.236067978

Solving
-2 + x = -2.236067978

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 = -2.236067978 + 2

Combine like terms: -2 + 2 = 0
0 + x = -2.236067978 + 2
x = -2.236067978 + 2

Combine like terms: -2.236067978 + 2 = -0.236067978
x = -0.236067978

Simplifying
x = -0.236067978

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {4.236067978, -0.236067978}
Solution
x = {4.236067978, -0.236067978}