10(x-1)+7y-(x+1)(x-1)=x(x-1)+1

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Solution for 10(x-1)+7y-(x+1)(x-1)=x(x-1)+1 equation: 


Simplifying
10(x + -1) + 7y + -1(x + 1)(x + -1) = x(x + -1) + 1

Reorder the terms:
10(-1 + x) + 7y + -1(x + 1)(x + -1) = x(x + -1) + 1
(-1 * 10 + x * 10) + 7y + -1(x + 1)(x + -1) = x(x + -1) + 1
(-10 + 10x) + 7y + -1(x + 1)(x + -1) = x(x + -1) + 1

Reorder the terms:
-10 + 10x + 7y + -1(1 + x)(x + -1) = x(x + -1) + 1

Reorder the terms:
-10 + 10x + 7y + -1(1 + x)(-1 + x) = x(x + -1) + 1

Multiply (1 + x) * (-1 + x)
-10 + 10x + 7y + -1(1(-1 + x) + x(-1 + x)) = x(x + -1) + 1
-10 + 10x + 7y + -1((-1 * 1 + x * 1) + x(-1 + x)) = x(x + -1) + 1
-10 + 10x + 7y + -1((-1 + 1x) + x(-1 + x)) = x(x + -1) + 1
-10 + 10x + 7y + -1(-1 + 1x + (-1 * x + x * x)) = x(x + -1) + 1
-10 + 10x + 7y + -1(-1 + 1x + (-1x + x2)) = x(x + -1) + 1

Combine like terms: 1x + -1x = 0
-10 + 10x + 7y + -1(-1 + 0 + x2) = x(x + -1) + 1
-10 + 10x + 7y + -1(-1 + x2) = x(x + -1) + 1
-10 + 10x + 7y + (-1 * -1 + x2 * -1) = x(x + -1) + 1
-10 + 10x + 7y + (1 + -1x2) = x(x + -1) + 1

Reorder the terms:
-10 + 1 + 10x + -1x2 + 7y = x(x + -1) + 1

Combine like terms: -10 + 1 = -9
-9 + 10x + -1x2 + 7y = x(x + -1) + 1

Reorder the terms:
-9 + 10x + -1x2 + 7y = x(-1 + x) + 1
-9 + 10x + -1x2 + 7y = (-1 * x + x * x) + 1
-9 + 10x + -1x2 + 7y = (-1x + x2) + 1

Reorder the terms:
-9 + 10x + -1x2 + 7y = 1 + -1x + x2

Solving
-9 + 10x + -1x2 + 7y = 1 + -1x + x2

Solving for variable 'x'.

Reorder the terms:
-9 + -1 + 10x + x + -1x2 + -1x2 + 7y = 1 + -1x + x2 + -1 + x + -1x2

Combine like terms: -9 + -1 = -10
-10 + 10x + x + -1x2 + -1x2 + 7y = 1 + -1x + x2 + -1 + x + -1x2

Combine like terms: 10x + x = 11x
-10 + 11x + -1x2 + -1x2 + 7y = 1 + -1x + x2 + -1 + x + -1x2

Combine like terms: -1x2 + -1x2 = -2x2
-10 + 11x + -2x2 + 7y = 1 + -1x + x2 + -1 + x + -1x2

Reorder the terms:
-10 + 11x + -2x2 + 7y = 1 + -1 + -1x + x + x2 + -1x2

Combine like terms: 1 + -1 = 0
-10 + 11x + -2x2 + 7y = 0 + -1x + x + x2 + -1x2
-10 + 11x + -2x2 + 7y = -1x + x + x2 + -1x2

Combine like terms: -1x + x = 0
-10 + 11x + -2x2 + 7y = 0 + x2 + -1x2
-10 + 11x + -2x2 + 7y = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
-10 + 11x + -2x2 + 7y = 0

The solution to this equation could not be determined.

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