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

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


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

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

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

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

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

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

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

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

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

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

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

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

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

Reorder the terms:
3 + -2x = 1 + -2x

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

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

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

Solving
3 = 1

Couldn't find a variable to solve for.

This equation is invalid, the left and right sides are not equal, therefore there is no solution.

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