(y-1)+5(x-1)-(3-x^2)=(x+1)(x-4)+5x-6

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Solution for (y-1)+5(x-1)-(3-x^2)=(x+1)(x-4)+5x-6 equation: 


Simplifying
(y + -1) + 5(x + -1) + -1(3 + -1x2) = (x + 1)(x + -4) + 5x + -6

Reorder the terms:
(-1 + y) + 5(x + -1) + -1(3 + -1x2) = (x + 1)(x + -4) + 5x + -6

Remove parenthesis around (-1 + y)
-1 + y + 5(x + -1) + -1(3 + -1x2) = (x + 1)(x + -4) + 5x + -6

Reorder the terms:
-1 + y + 5(-1 + x) + -1(3 + -1x2) = (x + 1)(x + -4) + 5x + -6
-1 + y + (-1 * 5 + x * 5) + -1(3 + -1x2) = (x + 1)(x + -4) + 5x + -6
-1 + y + (-5 + 5x) + -1(3 + -1x2) = (x + 1)(x + -4) + 5x + -6
-1 + y + -5 + 5x + (3 * -1 + -1x2 * -1) = (x + 1)(x + -4) + 5x + -6
-1 + y + -5 + 5x + (-3 + 1x2) = (x + 1)(x + -4) + 5x + -6

Reorder the terms:
-1 + -5 + -3 + 5x + 1x2 + y = (x + 1)(x + -4) + 5x + -6

Combine like terms: -1 + -5 = -6
-6 + -3 + 5x + 1x2 + y = (x + 1)(x + -4) + 5x + -6

Combine like terms: -6 + -3 = -9
-9 + 5x + 1x2 + y = (x + 1)(x + -4) + 5x + -6

Reorder the terms:
-9 + 5x + 1x2 + y = (1 + x)(x + -4) + 5x + -6

Reorder the terms:
-9 + 5x + 1x2 + y = (1 + x)(-4 + x) + 5x + -6

Multiply (1 + x) * (-4 + x)
-9 + 5x + 1x2 + y = (1(-4 + x) + x(-4 + x)) + 5x + -6
-9 + 5x + 1x2 + y = ((-4 * 1 + x * 1) + x(-4 + x)) + 5x + -6
-9 + 5x + 1x2 + y = ((-4 + 1x) + x(-4 + x)) + 5x + -6
-9 + 5x + 1x2 + y = (-4 + 1x + (-4 * x + x * x)) + 5x + -6
-9 + 5x + 1x2 + y = (-4 + 1x + (-4x + x2)) + 5x + -6

Combine like terms: 1x + -4x = -3x
-9 + 5x + 1x2 + y = (-4 + -3x + x2) + 5x + -6

Reorder the terms:
-9 + 5x + 1x2 + y = -4 + -6 + -3x + 5x + x2

Combine like terms: -4 + -6 = -10
-9 + 5x + 1x2 + y = -10 + -3x + 5x + x2

Combine like terms: -3x + 5x = 2x
-9 + 5x + 1x2 + y = -10 + 2x + x2

Solving
-9 + 5x + 1x2 + y = -10 + 2x + x2

Solving for variable 'x'.

Reorder the terms:
-9 + 10 + 5x + -2x + 1x2 + -1x2 + y = -10 + 2x + x2 + 10 + -2x + -1x2

Combine like terms: -9 + 10 = 1
1 + 5x + -2x + 1x2 + -1x2 + y = -10 + 2x + x2 + 10 + -2x + -1x2

Combine like terms: 5x + -2x = 3x
1 + 3x + 1x2 + -1x2 + y = -10 + 2x + x2 + 10 + -2x + -1x2

Combine like terms: 1x2 + -1x2 = 0
1 + 3x + 0 + y = -10 + 2x + x2 + 10 + -2x + -1x2
1 + 3x + y = -10 + 2x + x2 + 10 + -2x + -1x2

Reorder the terms:
1 + 3x + y = -10 + 10 + 2x + -2x + x2 + -1x2

Combine like terms: -10 + 10 = 0
1 + 3x + y = 0 + 2x + -2x + x2 + -1x2
1 + 3x + y = 2x + -2x + x2 + -1x2

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

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

The solution to this equation could not be determined.

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