x(x-1)-4=(x-2)(x+2)-x

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Solution for x(x-1)-4=(x-2)(x+2)-x equation:


Simplifying
x(x + -1) + -4 = (x + -2)(x + 2) + -1x

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

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

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

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

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

Combine like terms: -2x + 2x = 0
-4 + -1x + x2 = (-4 + 0 + x2) + -1x
-4 + -1x + x2 = (-4 + x2) + -1x

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

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

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

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

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

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

Add 'x' to each side of the equation.
-1x + x + x2 = -1x + x + x2

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

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

Add '-1x2' to each side of the equation.
x2 + -1x2 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = x2 + -1x2

Combine like terms: x2 + -1x2 = 0
0 = 0

Solving
0 = 0

Couldn't find a variable to solve for.

This equation is an identity, all real numbers are solutions.

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