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

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

Simplifying
2(5 + -3x) * 6x + -4(3 + -1x) = 0

Reorder the terms for easier multiplication:
2 * 6x(5 + -3x) + -4(3 + -1x) = 0

Multiply 2 * 6
12x(5 + -3x) + -4(3 + -1x) = 0
(5 * 12x + -3x * 12x) + -4(3 + -1x) = 0
(60x + -36x2) + -4(3 + -1x) = 0
60x + -36x2 + (3 * -4 + -1x * -4) = 0
60x + -36x2 + (-12 + 4x) = 0

Reorder the terms:
-12 + 60x + 4x + -36x2 = 0

Combine like terms: 60x + 4x = 64x
-12 + 64x + -36x2 = 0

Solving
-12 + 64x + -36x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-3 + 16x + -9x2) = 0

Ignore the factor 4.
Subproblem 1
Set the factor '(-3 + 16x + -9x2)' equal to zero and attempt to solve:

Simplifying
-3 + 16x + -9x2 = 0

Solving
-3 + 16x + -9x2 = 0

Begin completing the square.  Divide all terms by
-9 the coefficient of the squared term: 

Divide each side by '-9'.
0.3333333333 + -1.777777778x + x2 = 0

Move the constant term to the right:

Add '-0.3333333333' to each side of the equation.
0.3333333333 + -1.777777778x + -0.3333333333 + x2 = 0 + -0.3333333333

Reorder the terms:
0.3333333333 + -0.3333333333 + -1.777777778x + x2 = 0 + -0.3333333333

Combine like terms: 0.3333333333 + -0.3333333333 = 0.0000000000
0.0000000000 + -1.777777778x + x2 = 0 + -0.3333333333
-1.777777778x + x2 = 0 + -0.3333333333

Combine like terms: 0 + -0.3333333333 = -0.3333333333
-1.777777778x + x2 = -0.3333333333

The x term is -1.777777778x.  Take half its coefficient (-0.888888889).
Square it (0.7901234570) and add it to both sides.

Add '0.7901234570' to each side of the equation.
-1.777777778x + 0.7901234570 + x2 = -0.3333333333 + 0.7901234570

Reorder the terms:
0.7901234570 + -1.777777778x + x2 = -0.3333333333 + 0.7901234570

Combine like terms: -0.3333333333 + 0.7901234570 = 0.4567901237
0.7901234570 + -1.777777778x + x2 = 0.4567901237

Factor a perfect square on the left side:
(x + -0.888888889)(x + -0.888888889) = 0.4567901237

Calculate the square root of the right side: 0.675862504

Break this problem into two subproblems by setting 
(x + -0.888888889) equal to 0.675862504 and -0.675862504.

Subproblem 1
x + -0.888888889 = 0.675862504

Simplifying
x + -0.888888889 = 0.675862504

Reorder the terms:
-0.888888889 + x = 0.675862504

Solving
-0.888888889 + x = 0.675862504

Solving for variable 'x'.

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

Add '0.888888889' to each side of the equation.
-0.888888889 + 0.888888889 + x = 0.675862504 + 0.888888889

Combine like terms: -0.888888889 + 0.888888889 = 0.000000000
0.000000000 + x = 0.675862504 + 0.888888889
x = 0.675862504 + 0.888888889

Combine like terms: 0.675862504 + 0.888888889 = 1.564751393
x = 1.564751393

Simplifying
x = 1.564751393

Subproblem 2
x + -0.888888889 = -0.675862504

Simplifying
x + -0.888888889 = -0.675862504

Reorder the terms:
-0.888888889 + x = -0.675862504

Solving
-0.888888889 + x = -0.675862504

Solving for variable 'x'.

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

Add '0.888888889' to each side of the equation.
-0.888888889 + 0.888888889 + x = -0.675862504 + 0.888888889

Combine like terms: -0.888888889 + 0.888888889 = 0.000000000
0.000000000 + x = -0.675862504 + 0.888888889
x = -0.675862504 + 0.888888889

Combine like terms: -0.675862504 + 0.888888889 = 0.213026385
x = 0.213026385

Simplifying
x = 0.213026385

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {1.564751393, 0.213026385}
Solution
x = {1.564751393, 0.213026385}