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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

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

Solving
24 + -12x = 0

Solving for variable 'x'.

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

Add '-24' to each side of the equation.
24 + -24 + -12x = 0 + -24

Combine like terms: 24 + -24 = 0
0 + -12x = 0 + -24
-12x = 0 + -24

Combine like terms: 0 + -24 = -24
-12x = -24

Divide each side by '-12'.
x = 2

Simplifying
x = 2

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