(2x-1)(x-1)=(x-5)(2x-5)

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Solution for (2x-1)(x-1)=(x-5)(2x-5) equation: 


Simplifying
(2x + -1)(x + -1) = (x + -5)(2x + -5)

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

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

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

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

Reorder the terms:
1 + -3x + 2x2 = (-5 + x)(2x + -5)

Reorder the terms:
1 + -3x + 2x2 = (-5 + x)(-5 + 2x)

Multiply (-5 + x) * (-5 + 2x)
1 + -3x + 2x2 = (-5(-5 + 2x) + x(-5 + 2x))
1 + -3x + 2x2 = ((-5 * -5 + 2x * -5) + x(-5 + 2x))
1 + -3x + 2x2 = ((25 + -10x) + x(-5 + 2x))
1 + -3x + 2x2 = (25 + -10x + (-5 * x + 2x * x))
1 + -3x + 2x2 = (25 + -10x + (-5x + 2x2))

Combine like terms: -10x + -5x = -15x
1 + -3x + 2x2 = (25 + -15x + 2x2)

Add '-2x2' to each side of the equation.
1 + -3x + 2x2 + -2x2 = 25 + -15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + -3x + 0 = 25 + -15x + 2x2 + -2x2
1 + -3x = 25 + -15x + 2x2 + -2x2

Combine like terms: 2x2 + -2x2 = 0
1 + -3x = 25 + -15x + 0
1 + -3x = 25 + -15x

Solving
1 + -3x = 25 + -15x

Solving for variable 'x'.

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

Add '15x' to each side of the equation.
1 + -3x + 15x = 25 + -15x + 15x

Combine like terms: -3x + 15x = 12x
1 + 12x = 25 + -15x + 15x

Combine like terms: -15x + 15x = 0
1 + 12x = 25 + 0
1 + 12x = 25

Add '-1' to each side of the equation.
1 + -1 + 12x = 25 + -1

Combine like terms: 1 + -1 = 0
0 + 12x = 25 + -1
12x = 25 + -1

Combine like terms: 25 + -1 = 24
12x = 24

Divide each side by '12'.
x = 2

Simplifying
x = 2

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