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

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


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

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

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

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

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

Reorder the terms:
12 + -10x + 2x2 = (-1 + x)(x + -2)

Reorder the terms:
12 + -10x + 2x2 = (-1 + x)(-2 + x)

Multiply (-1 + x) * (-2 + x)
12 + -10x + 2x2 = (-1(-2 + x) + x(-2 + x))
12 + -10x + 2x2 = ((-2 * -1 + x * -1) + x(-2 + x))
12 + -10x + 2x2 = ((2 + -1x) + x(-2 + x))
12 + -10x + 2x2 = (2 + -1x + (-2 * x + x * x))
12 + -10x + 2x2 = (2 + -1x + (-2x + x2))

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

Solving
12 + -10x + 2x2 = 2 + -3x + x2

Solving for variable 'x'.

Reorder the terms:
12 + -2 + -10x + 3x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: 12 + -2 = 10
10 + -10x + 3x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: -10x + 3x = -7x
10 + -7x + 2x2 + -1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Combine like terms: 2x2 + -1x2 = 1x2
10 + -7x + 1x2 = 2 + -3x + x2 + -2 + 3x + -1x2

Reorder the terms:
10 + -7x + 1x2 = 2 + -2 + -3x + 3x + x2 + -1x2

Combine like terms: 2 + -2 = 0
10 + -7x + 1x2 = 0 + -3x + 3x + x2 + -1x2
10 + -7x + 1x2 = -3x + 3x + x2 + -1x2

Combine like terms: -3x + 3x = 0
10 + -7x + 1x2 = 0 + x2 + -1x2
10 + -7x + 1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
10 + -7x + 1x2 = 0

Factor a trinomial.
(2 + -1x)(5 + -1x) = 0


Subproblem 1
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

Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

Solving
5 + -1x = 0

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

Add '-5' to each side of the equation.
5 + -5 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {2, 5}

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