3x(x-2)-(x-6)=25(x-3)

Solution for 3x(x-2)-(x-6)=25(x-3) equation:

Simplifying
3x(x + -2) + -1(x + -6) = 25(x + -3)

Reorder the terms:
3x(-2 + x) + -1(x + -6) = 25(x + -3)
(-2 * 3x + x * 3x) + -1(x + -6) = 25(x + -3)
(-6x + 3x2) + -1(x + -6) = 25(x + -3)

Reorder the terms:
-6x + 3x2 + -1(-6 + x) = 25(x + -3)
-6x + 3x2 + (-6 * -1 + x * -1) = 25(x + -3)
-6x + 3x2 + (6 + -1x) = 25(x + -3)

Reorder the terms:
6 + -6x + -1x + 3x2 = 25(x + -3)

Combine like terms: -6x + -1x = -7x
6 + -7x + 3x2 = 25(x + -3)

Reorder the terms:
6 + -7x + 3x2 = 25(-3 + x)
6 + -7x + 3x2 = (-3 * 25 + x * 25)
6 + -7x + 3x2 = (-75 + 25x)

Solving
6 + -7x + 3x2 = -75 + 25x

Solving for variable 'x'.

Reorder the terms:
6 + 75 + -7x + -25x + 3x2 = -75 + 25x + 75 + -25x

Combine like terms: 6 + 75 = 81
81 + -7x + -25x + 3x2 = -75 + 25x + 75 + -25x

Combine like terms: -7x + -25x = -32x
81 + -32x + 3x2 = -75 + 25x + 75 + -25x

Reorder the terms:
81 + -32x + 3x2 = -75 + 75 + 25x + -25x

Combine like terms: -75 + 75 = 0
81 + -32x + 3x2 = 0 + 25x + -25x
81 + -32x + 3x2 = 25x + -25x

Combine like terms: 25x + -25x = 0
81 + -32x + 3x2 = 0

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

Divide each side by '3'.
27 + -10.66666667x + x2 = 0

Move the constant term to the right:

Add '-27' to each side of the equation.
27 + -10.66666667x + -27 + x2 = 0 + -27

Reorder the terms:
27 + -27 + -10.66666667x + x2 = 0 + -27

Combine like terms: 27 + -27 = 0
0 + -10.66666667x + x2 = 0 + -27
-10.66666667x + x2 = 0 + -27

Combine like terms: 0 + -27 = -27
-10.66666667x + x2 = -27

The x term is -10.66666667x.  Take half its coefficient (-5.333333335).
Square it (28.44444446) and add it to both sides.

Add '28.44444446' to each side of the equation.
-10.66666667x + 28.44444446 + x2 = -27 + 28.44444446

Reorder the terms:
28.44444446 + -10.66666667x + x2 = -27 + 28.44444446

Combine like terms: -27 + 28.44444446 = 1.44444446
28.44444446 + -10.66666667x + x2 = 1.44444446

Factor a perfect square on the left side:
(x + -5.333333335)(x + -5.333333335) = 1.44444446

Calculate the square root of the right side: 1.201850432

Break this problem into two subproblems by setting 
(x + -5.333333335) equal to 1.201850432 and -1.201850432.

Subproblem 1
x + -5.333333335 = 1.201850432

Simplifying
x + -5.333333335 = 1.201850432

Reorder the terms:
-5.333333335 + x = 1.201850432

Solving
-5.333333335 + x = 1.201850432

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = 1.201850432 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = 1.201850432 + 5.333333335
x = 1.201850432 + 5.333333335

Combine like terms: 1.201850432 + 5.333333335 = 6.535183767
x = 6.535183767

Simplifying
x = 6.535183767

Subproblem 2
x + -5.333333335 = -1.201850432

Simplifying
x + -5.333333335 = -1.201850432

Reorder the terms:
-5.333333335 + x = -1.201850432

Solving
-5.333333335 + x = -1.201850432

Solving for variable 'x'.

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

Add '5.333333335' to each side of the equation.
-5.333333335 + 5.333333335 + x = -1.201850432 + 5.333333335

Combine like terms: -5.333333335 + 5.333333335 = 0.000000000
0.000000000 + x = -1.201850432 + 5.333333335
x = -1.201850432 + 5.333333335

Combine like terms: -1.201850432 + 5.333333335 = 4.131482903
x = 4.131482903

Simplifying
x = 4.131482903

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {6.535183767, 4.131482903}