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

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


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

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

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

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

Combine like terms: -3x + -2x = -5x
(1 + -5x + 6x2) = (x + 1)(4x + -2)

Reorder the terms:
1 + -5x + 6x2 = (1 + x)(4x + -2)

Reorder the terms:
1 + -5x + 6x2 = (1 + x)(-2 + 4x)

Multiply (1 + x) * (-2 + 4x)
1 + -5x + 6x2 = (1(-2 + 4x) + x(-2 + 4x))
1 + -5x + 6x2 = ((-2 * 1 + 4x * 1) + x(-2 + 4x))
1 + -5x + 6x2 = ((-2 + 4x) + x(-2 + 4x))
1 + -5x + 6x2 = (-2 + 4x + (-2 * x + 4x * x))
1 + -5x + 6x2 = (-2 + 4x + (-2x + 4x2))

Combine like terms: 4x + -2x = 2x
1 + -5x + 6x2 = (-2 + 2x + 4x2)

Solving
1 + -5x + 6x2 = -2 + 2x + 4x2

Solving for variable 'x'.

Reorder the terms:
1 + 2 + -5x + -2x + 6x2 + -4x2 = -2 + 2x + 4x2 + 2 + -2x + -4x2

Combine like terms: 1 + 2 = 3
3 + -5x + -2x + 6x2 + -4x2 = -2 + 2x + 4x2 + 2 + -2x + -4x2

Combine like terms: -5x + -2x = -7x
3 + -7x + 6x2 + -4x2 = -2 + 2x + 4x2 + 2 + -2x + -4x2

Combine like terms: 6x2 + -4x2 = 2x2
3 + -7x + 2x2 = -2 + 2x + 4x2 + 2 + -2x + -4x2

Reorder the terms:
3 + -7x + 2x2 = -2 + 2 + 2x + -2x + 4x2 + -4x2

Combine like terms: -2 + 2 = 0
3 + -7x + 2x2 = 0 + 2x + -2x + 4x2 + -4x2
3 + -7x + 2x2 = 2x + -2x + 4x2 + -4x2

Combine like terms: 2x + -2x = 0
3 + -7x + 2x2 = 0 + 4x2 + -4x2
3 + -7x + 2x2 = 4x2 + -4x2

Combine like terms: 4x2 + -4x2 = 0
3 + -7x + 2x2 = 0

Factor a trinomial.
(1 + -2x)(3 + -1x) = 0


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

Simplifying
1 + -2x = 0

Solving
1 + -2x = 0

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

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

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

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

Divide each side by '-2'.
x = 0.5

Simplifying
x = 0.5

Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 0

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

Add '-3' to each side of the equation.
3 + -3 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {0.5, 3}

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