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

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


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

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

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

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

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

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

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

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

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

Add '-1x2' to each side of the equation.
2 + -3x + x2 + -1x2 = -5 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x + 0 = -5 + -4x + x2 + -1x2
2 + -3x = -5 + -4x + x2 + -1x2

Combine like terms: x2 + -1x2 = 0
2 + -3x = -5 + -4x + 0
2 + -3x = -5 + -4x

Solving
2 + -3x = -5 + -4x

Solving for variable 'x'.

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

Add '4x' to each side of the equation.
2 + -3x + 4x = -5 + -4x + 4x

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

Combine like terms: -4x + 4x = 0
2 + 1x = -5 + 0
2 + 1x = -5

Add '-2' to each side of the equation.
2 + -2 + 1x = -5 + -2

Combine like terms: 2 + -2 = 0
0 + 1x = -5 + -2
1x = -5 + -2

Combine like terms: -5 + -2 = -7
1x = -7

Divide each side by '1'.
x = -7

Simplifying
x = -7

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