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

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

Simplifying
6x(6 + -1x + -4(x + -6)) = (2x + -5)(5x + -2)

Reorder the terms:
6x(6 + -1x + -4(-6 + x)) = (2x + -5)(5x + -2)
6x(6 + -1x + (-6 * -4 + x * -4)) = (2x + -5)(5x + -2)
6x(6 + -1x + (24 + -4x)) = (2x + -5)(5x + -2)

Reorder the terms:
6x(6 + 24 + -1x + -4x) = (2x + -5)(5x + -2)

Combine like terms: 6 + 24 = 30
6x(30 + -1x + -4x) = (2x + -5)(5x + -2)

Combine like terms: -1x + -4x = -5x
6x(30 + -5x) = (2x + -5)(5x + -2)
(30 * 6x + -5x * 6x) = (2x + -5)(5x + -2)
(180x + -30x2) = (2x + -5)(5x + -2)

Reorder the terms:
180x + -30x2 = (-5 + 2x)(5x + -2)

Reorder the terms:
180x + -30x2 = (-5 + 2x)(-2 + 5x)

Multiply (-5 + 2x) * (-2 + 5x)
180x + -30x2 = (-5(-2 + 5x) + 2x * (-2 + 5x))
180x + -30x2 = ((-2 * -5 + 5x * -5) + 2x * (-2 + 5x))
180x + -30x2 = ((10 + -25x) + 2x * (-2 + 5x))
180x + -30x2 = (10 + -25x + (-2 * 2x + 5x * 2x))
180x + -30x2 = (10 + -25x + (-4x + 10x2))

Combine like terms: -25x + -4x = -29x
180x + -30x2 = (10 + -29x + 10x2)

Solving
180x + -30x2 = 10 + -29x + 10x2

Solving for variable 'x'.

Reorder the terms:
-10 + 180x + 29x + -30x2 + -10x2 = 10 + -29x + 10x2 + -10 + 29x + -10x2

Combine like terms: 180x + 29x = 209x
-10 + 209x + -30x2 + -10x2 = 10 + -29x + 10x2 + -10 + 29x + -10x2

Combine like terms: -30x2 + -10x2 = -40x2
-10 + 209x + -40x2 = 10 + -29x + 10x2 + -10 + 29x + -10x2

Reorder the terms:
-10 + 209x + -40x2 = 10 + -10 + -29x + 29x + 10x2 + -10x2

Combine like terms: 10 + -10 = 0
-10 + 209x + -40x2 = 0 + -29x + 29x + 10x2 + -10x2
-10 + 209x + -40x2 = -29x + 29x + 10x2 + -10x2

Combine like terms: -29x + 29x = 0
-10 + 209x + -40x2 = 0 + 10x2 + -10x2
-10 + 209x + -40x2 = 10x2 + -10x2

Combine like terms: 10x2 + -10x2 = 0
-10 + 209x + -40x2 = 0

Begin completing the square.  Divide all terms by
-40 the coefficient of the squared term: 

Divide each side by '-40'.
0.25 + -5.225x + x2 = 0

Move the constant term to the right:

Add '-0.25' to each side of the equation.
0.25 + -5.225x + -0.25 + x2 = 0 + -0.25

Reorder the terms:
0.25 + -0.25 + -5.225x + x2 = 0 + -0.25

Combine like terms: 0.25 + -0.25 = 0.00
0.00 + -5.225x + x2 = 0 + -0.25
-5.225x + x2 = 0 + -0.25

Combine like terms: 0 + -0.25 = -0.25
-5.225x + x2 = -0.25

The x term is -5.225x.  Take half its coefficient (-2.6125).
Square it (6.82515625) and add it to both sides.

Add '6.82515625' to each side of the equation.
-5.225x + 6.82515625 + x2 = -0.25 + 6.82515625

Reorder the terms:
6.82515625 + -5.225x + x2 = -0.25 + 6.82515625

Combine like terms: -0.25 + 6.82515625 = 6.57515625
6.82515625 + -5.225x + x2 = 6.57515625

Factor a perfect square on the left side:
(x + -2.6125)(x + -2.6125) = 6.57515625

Calculate the square root of the right side: 2.564206749

Break this problem into two subproblems by setting 
(x + -2.6125) equal to 2.564206749 and -2.564206749.

Subproblem 1
x + -2.6125 = 2.564206749

Simplifying
x + -2.6125 = 2.564206749

Reorder the terms:
-2.6125 + x = 2.564206749

Solving
-2.6125 + x = 2.564206749

Solving for variable 'x'.

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

Add '2.6125' to each side of the equation.
-2.6125 + 2.6125 + x = 2.564206749 + 2.6125

Combine like terms: -2.6125 + 2.6125 = 0.0000
0.0000 + x = 2.564206749 + 2.6125
x = 2.564206749 + 2.6125

Combine like terms: 2.564206749 + 2.6125 = 5.176706749
x = 5.176706749

Simplifying
x = 5.176706749

Subproblem 2
x + -2.6125 = -2.564206749

Simplifying
x + -2.6125 = -2.564206749

Reorder the terms:
-2.6125 + x = -2.564206749

Solving
-2.6125 + x = -2.564206749

Solving for variable 'x'.

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

Add '2.6125' to each side of the equation.
-2.6125 + 2.6125 + x = -2.564206749 + 2.6125

Combine like terms: -2.6125 + 2.6125 = 0.0000
0.0000 + x = -2.564206749 + 2.6125
x = -2.564206749 + 2.6125

Combine like terms: -2.564206749 + 2.6125 = 0.048293251
x = 0.048293251

Simplifying
x = 0.048293251

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {5.176706749, 0.048293251}