4[3+5(3-x)2x]=6-2x

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

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

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

Multiply 5 * 2
4[3 + 10x(3 + -1x)] = 6 + -2x
4[3 + (3 * 10x + -1x * 10x)] = 6 + -2x
4[3 + (30x + -10x2)] = 6 + -2x
[3 * 4 + 30x * 4 + -10x2 * 4] = 6 + -2x
[12 + 120x + -40x2] = 6 + -2x

Solving
12 + 120x + -40x2 = 6 + -2x

Solving for variable 'x'.

Reorder the terms:
12 + -6 + 120x + 2x + -40x2 = 6 + -2x + -6 + 2x

Combine like terms: 12 + -6 = 6
6 + 120x + 2x + -40x2 = 6 + -2x + -6 + 2x

Combine like terms: 120x + 2x = 122x
6 + 122x + -40x2 = 6 + -2x + -6 + 2x

Reorder the terms:
6 + 122x + -40x2 = 6 + -6 + -2x + 2x

Combine like terms: 6 + -6 = 0
6 + 122x + -40x2 = 0 + -2x + 2x
6 + 122x + -40x2 = -2x + 2x

Combine like terms: -2x + 2x = 0
6 + 122x + -40x2 = 0

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + 61x + -20x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3 + 61x + -20x2)' equal to zero and attempt to solve:

Simplifying
3 + 61x + -20x2 = 0

Solving
3 + 61x + -20x2 = 0

Begin completing the square.  Divide all terms by
-20 the coefficient of the squared term: 

Divide each side by '-20'.
-0.15 + -3.05x + x2 = 0.0

Move the constant term to the right:

Add '0.15' to each side of the equation.
-0.15 + -3.05x + 0.15 + x2 = 0.0 + 0.15

Reorder the terms:
-0.15 + 0.15 + -3.05x + x2 = 0.0 + 0.15

Combine like terms: -0.15 + 0.15 = 0.00
0.00 + -3.05x + x2 = 0.0 + 0.15
-3.05x + x2 = 0.0 + 0.15

Combine like terms: 0.0 + 0.15 = 0.15
-3.05x + x2 = 0.15

The x term is -3.05x.  Take half its coefficient (-1.525).
Square it (2.325625) and add it to both sides.

Add '2.325625' to each side of the equation.
-3.05x + 2.325625 + x2 = 0.15 + 2.325625

Reorder the terms:
2.325625 + -3.05x + x2 = 0.15 + 2.325625

Combine like terms: 0.15 + 2.325625 = 2.475625
2.325625 + -3.05x + x2 = 2.475625

Factor a perfect square on the left side:
(x + -1.525)(x + -1.525) = 2.475625

Calculate the square root of the right side: 1.573411898

Break this problem into two subproblems by setting 
(x + -1.525) equal to 1.573411898 and -1.573411898.

Subproblem 1
x + -1.525 = 1.573411898

Simplifying
x + -1.525 = 1.573411898

Reorder the terms:
-1.525 + x = 1.573411898

Solving
-1.525 + x = 1.573411898

Solving for variable 'x'.

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

Add '1.525' to each side of the equation.
-1.525 + 1.525 + x = 1.573411898 + 1.525

Combine like terms: -1.525 + 1.525 = 0.000
0.000 + x = 1.573411898 + 1.525
x = 1.573411898 + 1.525

Combine like terms: 1.573411898 + 1.525 = 3.098411898
x = 3.098411898

Simplifying
x = 3.098411898

Subproblem 2
x + -1.525 = -1.573411898

Simplifying
x + -1.525 = -1.573411898

Reorder the terms:
-1.525 + x = -1.573411898

Solving
-1.525 + x = -1.573411898

Solving for variable 'x'.

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

Add '1.525' to each side of the equation.
-1.525 + 1.525 + x = -1.573411898 + 1.525

Combine like terms: -1.525 + 1.525 = 0.000
0.000 + x = -1.573411898 + 1.525
x = -1.573411898 + 1.525

Combine like terms: -1.573411898 + 1.525 = -0.048411898
x = -0.048411898

Simplifying
x = -0.048411898

Solution
The solution to the problem is based on the solutions
from the subproblems.
x = {3.098411898, -0.048411898}
Solution
x = {3.098411898, -0.048411898}