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

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


Simplifying
2(3x + -1) + -2x(x + -1) = 3x2 + -4x + 2

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

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

Combine like terms: 6x + 2x = 8x
-2 + 8x + -2x2 = 3x2 + -4x + 2

Reorder the terms:
-2 + 8x + -2x2 = 2 + -4x + 3x2

Solving
-2 + 8x + -2x2 = 2 + -4x + 3x2

Solving for variable 'x'.

Reorder the terms:
-2 + -2 + 8x + 4x + -2x2 + -3x2 = 2 + -4x + 3x2 + -2 + 4x + -3x2

Combine like terms: -2 + -2 = -4
-4 + 8x + 4x + -2x2 + -3x2 = 2 + -4x + 3x2 + -2 + 4x + -3x2

Combine like terms: 8x + 4x = 12x
-4 + 12x + -2x2 + -3x2 = 2 + -4x + 3x2 + -2 + 4x + -3x2

Combine like terms: -2x2 + -3x2 = -5x2
-4 + 12x + -5x2 = 2 + -4x + 3x2 + -2 + 4x + -3x2

Reorder the terms:
-4 + 12x + -5x2 = 2 + -2 + -4x + 4x + 3x2 + -3x2

Combine like terms: 2 + -2 = 0
-4 + 12x + -5x2 = 0 + -4x + 4x + 3x2 + -3x2
-4 + 12x + -5x2 = -4x + 4x + 3x2 + -3x2

Combine like terms: -4x + 4x = 0
-4 + 12x + -5x2 = 0 + 3x2 + -3x2
-4 + 12x + -5x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
-4 + 12x + -5x2 = 0

Factor a trinomial.
(-2 + x)(2 + -5x) = 0


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

Simplifying
-2 + x = 0

Solving
-2 + x = 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 + x = 0 + 2

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

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

Simplifying
x = 2

Subproblem 2
Set the factor '(2 + -5x)' equal to zero and attempt to solve:

Simplifying
2 + -5x = 0

Solving
2 + -5x = 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 + -5x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -5x = 0 + -2
-5x = 0 + -2

Combine like terms: 0 + -2 = -2
-5x = -2

Divide each side by '-5'.
x = 0.4

Simplifying
x = 0.4
Solution
x = {2, 0.4}

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