(4-2x)x(3x+1)+(2x-4)x(x-2)-(4-2x)x(2x-3)=0

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Solution for (4-2x)x(3x+1)+(2x-4)x(x-2)-(4-2x)x(2x-3)=0 equation: 


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

Reorder the terms:
(4 + -2x) * x(1 + 3x) + (2x + -4) * x(x + -2) + -1(4 + -2x) * x(2x + -3) = 0

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

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

Combine like terms: 12x + -2x = 10x
x(4 + 10x + -6x2) + (2x + -4) * x(x + -2) + -1(4 + -2x) * x(2x + -3) = 0
(4 * x + 10x * x + -6x2 * x) + (2x + -4) * x(x + -2) + -1(4 + -2x) * x(2x + -3) = 0
(4x + 10x2 + -6x3) + (2x + -4) * x(x + -2) + -1(4 + -2x) * x(2x + -3) = 0

Reorder the terms:
4x + 10x2 + -6x3 + (-4 + 2x) * x(x + -2) + -1(4 + -2x) * x(2x + -3) = 0

Reorder the terms:
4x + 10x2 + -6x3 + (-4 + 2x) * x(-2 + x) + -1(4 + -2x) * x(2x + -3) = 0

Reorder the terms for easier multiplication:
4x + 10x2 + -6x3 + x(-4 + 2x)(-2 + x) + -1(4 + -2x) * x(2x + -3) = 0

Multiply (-4 + 2x) * (-2 + x)
4x + 10x2 + -6x3 + x(-4(-2 + x) + 2x * (-2 + x)) + -1(4 + -2x) * x(2x + -3) = 0
4x + 10x2 + -6x3 + x((-2 * -4 + x * -4) + 2x * (-2 + x)) + -1(4 + -2x) * x(2x + -3) = 0
4x + 10x2 + -6x3 + x((8 + -4x) + 2x * (-2 + x)) + -1(4 + -2x) * x(2x + -3) = 0
4x + 10x2 + -6x3 + x(8 + -4x + (-2 * 2x + x * 2x)) + -1(4 + -2x) * x(2x + -3) = 0
4x + 10x2 + -6x3 + x(8 + -4x + (-4x + 2x2)) + -1(4 + -2x) * x(2x + -3) = 0

Combine like terms: -4x + -4x = -8x
4x + 10x2 + -6x3 + x(8 + -8x + 2x2) + -1(4 + -2x) * x(2x + -3) = 0
4x + 10x2 + -6x3 + (8 * x + -8x * x + 2x2 * x) + -1(4 + -2x) * x(2x + -3) = 0
4x + 10x2 + -6x3 + (8x + -8x2 + 2x3) + -1(4 + -2x) * x(2x + -3) = 0

Reorder the terms:
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1(4 + -2x) * x(-3 + 2x) = 0

Reorder the terms for easier multiplication:
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x(4 + -2x)(-3 + 2x) = 0

Multiply (4 + -2x) * (-3 + 2x)
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x(4(-3 + 2x) + -2x * (-3 + 2x)) = 0
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x((-3 * 4 + 2x * 4) + -2x * (-3 + 2x)) = 0
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x((-12 + 8x) + -2x * (-3 + 2x)) = 0
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x(-12 + 8x + (-3 * -2x + 2x * -2x)) = 0
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x(-12 + 8x + (6x + -4x2)) = 0

Combine like terms: 8x + 6x = 14x
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + -1x(-12 + 14x + -4x2) = 0
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + (-12 * -1x + 14x * -1x + -4x2 * -1x) = 0
4x + 10x2 + -6x3 + 8x + -8x2 + 2x3 + (12x + -14x2 + 4x3) = 0

Reorder the terms:
4x + 8x + 12x + 10x2 + -8x2 + -14x2 + -6x3 + 2x3 + 4x3 = 0

Combine like terms: 4x + 8x = 12x
12x + 12x + 10x2 + -8x2 + -14x2 + -6x3 + 2x3 + 4x3 = 0

Combine like terms: 12x + 12x = 24x
24x + 10x2 + -8x2 + -14x2 + -6x3 + 2x3 + 4x3 = 0

Combine like terms: 10x2 + -8x2 = 2x2
24x + 2x2 + -14x2 + -6x3 + 2x3 + 4x3 = 0

Combine like terms: 2x2 + -14x2 = -12x2
24x + -12x2 + -6x3 + 2x3 + 4x3 = 0

Combine like terms: -6x3 + 2x3 = -4x3
24x + -12x2 + -4x3 + 4x3 = 0

Combine like terms: -4x3 + 4x3 = 0
24x + -12x2 + 0 = 0
24x + -12x2 = 0

Solving
24x + -12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '12x'.
12x(2 + -1x) = 0

Ignore the factor 12.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {0, 2}

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