2x(5x-3x(x+2)+3x^2)-2x^2(2-x(3-2x)-x^2+x)=

Solution for 2x(5x-3x(x+2)+3x^2)-2x^2(2-x(3-2x)-x^2+x)= equation:

Simplifying
2x(5x + -3x(x + 2) + 3x2) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Reorder the terms:
2x(5x + -3x(2 + x) + 3x2) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0
2x(5x + (2 * -3x + x * -3x) + 3x2) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0
2x(5x + (-6x + -3x2) + 3x2) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Combine like terms: 5x + -6x = -1x
2x(-1x + -3x2 + 3x2) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Combine like terms: -3x2 + 3x2 = 0
2x(-1x + 0) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0
2x(-1x) + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Remove parenthesis around (-1x)
2x * -1x + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Reorder the terms for easier multiplication:
2 * -1x * x + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Multiply 2 * -1
-2x * x + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0

Multiply x * x
-2x2 + -2x2(2 + -1x(3 + -2x) + -1x2 + x) = 0
-2x2 + -2x2(2 + (3 * -1x + -2x * -1x) + -1x2 + x) = 0
-2x2 + -2x2(2 + (-3x + 2x2) + -1x2 + x) = 0

Reorder the terms:
-2x2 + -2x2(2 + -3x + x + 2x2 + -1x2) = 0

Combine like terms: -3x + x = -2x
-2x2 + -2x2(2 + -2x + 2x2 + -1x2) = 0

Combine like terms: 2x2 + -1x2 = 1x2
-2x2 + -2x2(2 + -2x + 1x2) = 0
-2x2 + (2 * -2x2 + -2x * -2x2 + 1x2 * -2x2) = 0
-2x2 + (-4x2 + 4x3 + -2x4) = 0

Combine like terms: -2x2 + -4x2 = -6x2
-6x2 + 4x3 + -2x4 = 0

Solving
-6x2 + 4x3 + -2x4 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2x2'.
2x2(-3 + 2x + -1x2) = 0

Ignore the factor 2.
Subproblem 1
Set the factor 'x2' equal to zero and attempt to solve:

Simplifying
x2 = 0

Solving
x2 = 0

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

Simplifying
x2 = 0

Take the square root of each side:
x = {0}
Subproblem 2
Set the factor '(-3 + 2x + -1x2)' equal to zero and attempt to solve:

Simplifying
-3 + 2x + -1x2 = 0

Solving
-3 + 2x + -1x2 = 0

Begin completing the square.  Divide all terms by
-1 the coefficient of the squared term: 

Divide each side by '-1'.
3 + -2x + x2 = 0

Move the constant term to the right:

Add '-3' to each side of the equation.
3 + -2x + -3 + x2 = 0 + -3

Reorder the terms:
3 + -3 + -2x + x2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x + x2 = 0 + -3
-2x + x2 = 0 + -3

Combine like terms: 0 + -3 = -3
-2x + x2 = -3

The x term is -2x.  Take half its coefficient (-1).
Square it (1) and add it to both sides.

Add '1' to each side of the equation.
-2x + 1 + x2 = -3 + 1

Reorder the terms:
1 + -2x + x2 = -3 + 1

Combine like terms: -3 + 1 = -2
1 + -2x + x2 = -2

Factor a perfect square on the left side:
(x + -1)(x + -1) = -2

Can't calculate square root of the right side.

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}