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

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


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

Reorder the terms:
3(-4 + x) = (2x + -3)(x + -1)
(-4 * 3 + x * 3) = (2x + -3)(x + -1)
(-12 + 3x) = (2x + -3)(x + -1)

Reorder the terms:
-12 + 3x = (-3 + 2x)(x + -1)

Reorder the terms:
-12 + 3x = (-3 + 2x)(-1 + x)

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

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

Solving
-12 + 3x = 3 + -5x + 2x2

Solving for variable 'x'.

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

Combine like terms: -12 + -3 = -15
-15 + 3x + 5x + -2x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2

Combine like terms: 3x + 5x = 8x
-15 + 8x + -2x2 = 3 + -5x + 2x2 + -3 + 5x + -2x2

Reorder the terms:
-15 + 8x + -2x2 = 3 + -3 + -5x + 5x + 2x2 + -2x2

Combine like terms: 3 + -3 = 0
-15 + 8x + -2x2 = 0 + -5x + 5x + 2x2 + -2x2
-15 + 8x + -2x2 = -5x + 5x + 2x2 + -2x2

Combine like terms: -5x + 5x = 0
-15 + 8x + -2x2 = 0 + 2x2 + -2x2
-15 + 8x + -2x2 = 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
-15 + 8x + -2x2 = 0

Begin completing the square.  Divide all terms by
-2 the coefficient of the squared term: 

Divide each side by '-2'.
7.5 + -4x + x2 = 0

Move the constant term to the right:

Add '-7.5' to each side of the equation.
7.5 + -4x + -7.5 + x2 = 0 + -7.5

Reorder the terms:
7.5 + -7.5 + -4x + x2 = 0 + -7.5

Combine like terms: 7.5 + -7.5 = 0.0
0.0 + -4x + x2 = 0 + -7.5
-4x + x2 = 0 + -7.5

Combine like terms: 0 + -7.5 = -7.5
-4x + x2 = -7.5

The x term is -4x.  Take half its coefficient (-2).
Square it (4) and add it to both sides.

Add '4' to each side of the equation.
-4x + 4 + x2 = -7.5 + 4

Reorder the terms:
4 + -4x + x2 = -7.5 + 4

Combine like terms: -7.5 + 4 = -3.5
4 + -4x + x2 = -3.5

Factor a perfect square on the left side:
(x + -2)(x + -2) = -3.5

Can't calculate square root of the right side.

The solution to this equation could not be determined.

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