6x-3(6-5x)3x=10-4(2-x)

Solution for 6x-3(6-5x)3x=10-4(2-x) equation:

Simplifying
6x + -3(6 + -5x) * 3x = 10 + -4(2 + -1x)

Reorder the terms for easier multiplication:
6x + -3 * 3x(6 + -5x) = 10 + -4(2 + -1x)

Multiply -3 * 3
6x + -9x(6 + -5x) = 10 + -4(2 + -1x)
6x + (6 * -9x + -5x * -9x) = 10 + -4(2 + -1x)
6x + (-54x + 45x2) = 10 + -4(2 + -1x)

Combine like terms: 6x + -54x = -48x
-48x + 45x2 = 10 + -4(2 + -1x)
-48x + 45x2 = 10 + (2 * -4 + -1x * -4)
-48x + 45x2 = 10 + (-8 + 4x)

Combine like terms: 10 + -8 = 2
-48x + 45x2 = 2 + 4x

Solving
-48x + 45x2 = 2 + 4x

Solving for variable 'x'.

Reorder the terms:
-2 + -48x + -4x + 45x2 = 2 + 4x + -2 + -4x

Combine like terms: -48x + -4x = -52x
-2 + -52x + 45x2 = 2 + 4x + -2 + -4x

Reorder the terms:
-2 + -52x + 45x2 = 2 + -2 + 4x + -4x

Combine like terms: 2 + -2 = 0
-2 + -52x + 45x2 = 0 + 4x + -4x
-2 + -52x + 45x2 = 4x + -4x

Combine like terms: 4x + -4x = 0
-2 + -52x + 45x2 = 0

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

Divide each side by '45'.
-0.04444444444 + -1.155555556x + x2 = 0

Move the constant term to the right:

Add '0.04444444444' to each side of the equation.
-0.04444444444 + -1.155555556x + 0.04444444444 + x2 = 0 + 0.04444444444

Reorder the terms:
-0.04444444444 + 0.04444444444 + -1.155555556x + x2 = 0 + 0.04444444444

Combine like terms: -0.04444444444 + 0.04444444444 = 0.00000000000
0.00000000000 + -1.155555556x + x2 = 0 + 0.04444444444
-1.155555556x + x2 = 0 + 0.04444444444

Combine like terms: 0 + 0.04444444444 = 0.04444444444
-1.155555556x + x2 = 0.04444444444

The x term is -1.155555556x.  Take half its coefficient (-0.577777778).
Square it (0.3338271608) and add it to both sides.

Add '0.3338271608' to each side of the equation.
-1.155555556x + 0.3338271608 + x2 = 0.04444444444 + 0.3338271608

Reorder the terms:
0.3338271608 + -1.155555556x + x2 = 0.04444444444 + 0.3338271608

Combine like terms: 0.04444444444 + 0.3338271608 = 0.37827160524
0.3338271608 + -1.155555556x + x2 = 0.37827160524

Factor a perfect square on the left side:
(x + -0.577777778)(x + -0.577777778) = 0.37827160524

Calculate the square root of the right side: 0.615037889

Break this problem into two subproblems by setting 
(x + -0.577777778) equal to 0.615037889 and -0.615037889.

Subproblem 1
x + -0.577777778 = 0.615037889

Simplifying
x + -0.577777778 = 0.615037889

Reorder the terms:
-0.577777778 + x = 0.615037889

Solving
-0.577777778 + x = 0.615037889

Solving for variable 'x'.

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

Add '0.577777778' to each side of the equation.
-0.577777778 + 0.577777778 + x = 0.615037889 + 0.577777778

Combine like terms: -0.577777778 + 0.577777778 = 0.000000000
0.000000000 + x = 0.615037889 + 0.577777778
x = 0.615037889 + 0.577777778

Combine like terms: 0.615037889 + 0.577777778 = 1.192815667
x = 1.192815667

Simplifying
x = 1.192815667

Subproblem 2
x + -0.577777778 = -0.615037889

Simplifying
x + -0.577777778 = -0.615037889

Reorder the terms:
-0.577777778 + x = -0.615037889

Solving
-0.577777778 + x = -0.615037889

Solving for variable 'x'.

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

Add '0.577777778' to each side of the equation.
-0.577777778 + 0.577777778 + x = -0.615037889 + 0.577777778

Combine like terms: -0.577777778 + 0.577777778 = 0.000000000
0.000000000 + x = -0.615037889 + 0.577777778
x = -0.615037889 + 0.577777778

Combine like terms: -0.615037889 + 0.577777778 = -0.037260111
x = -0.037260111

Simplifying
x = -0.037260111

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.192815667, -0.037260111}