x^5-x^4-7x^3+7x^2+12x-12=(x-1)(x^4-7x^2+12)

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Solution for x^5-x^4-7x^3+7x^2+12x-12=(x-1)(x^4-7x^2+12) equation: 


Simplifying
x5 + -1x4 + -7x3 + 7x2 + 12x + -12 = (x + -1)(x4 + -7x2 + 12)

Reorder the terms:
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (x + -1)(x4 + -7x2 + 12)

Reorder the terms:
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-1 + x)(x4 + -7x2 + 12)

Reorder the terms:
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-1 + x)(12 + -7x2 + x4)

Multiply (-1 + x) * (12 + -7x2 + x4)
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-1(12 + -7x2 + x4) + x(12 + -7x2 + x4))
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = ((12 * -1 + -7x2 * -1 + x4 * -1) + x(12 + -7x2 + x4))
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = ((-12 + 7x2 + -1x4) + x(12 + -7x2 + x4))
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-12 + 7x2 + -1x4 + (12 * x + -7x2 * x + x4 * x))
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-12 + 7x2 + -1x4 + (12x + -7x3 + x5))

Reorder the terms:
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-12 + 12x + 7x2 + -7x3 + -1x4 + x5)
-12 + 12x + 7x2 + -7x3 + -1x4 + x5 = (-12 + 12x + 7x2 + -7x3 + -1x4 + x5)

Add '12' to each side of the equation.
-12 + 12x + 7x2 + -7x3 + -1x4 + 12 + x5 = -12 + 12x + 7x2 + -7x3 + -1x4 + 12 + x5

Reorder the terms:
-12 + 12 + 12x + 7x2 + -7x3 + -1x4 + x5 = -12 + 12x + 7x2 + -7x3 + -1x4 + 12 + x5

Combine like terms: -12 + 12 = 0
0 + 12x + 7x2 + -7x3 + -1x4 + x5 = -12 + 12x + 7x2 + -7x3 + -1x4 + 12 + x5
12x + 7x2 + -7x3 + -1x4 + x5 = -12 + 12x + 7x2 + -7x3 + -1x4 + 12 + x5

Reorder the terms:
12x + 7x2 + -7x3 + -1x4 + x5 = -12 + 12 + 12x + 7x2 + -7x3 + -1x4 + x5

Combine like terms: -12 + 12 = 0
12x + 7x2 + -7x3 + -1x4 + x5 = 0 + 12x + 7x2 + -7x3 + -1x4 + x5
12x + 7x2 + -7x3 + -1x4 + x5 = 12x + 7x2 + -7x3 + -1x4 + x5

Add '-12x' to each side of the equation.
12x + 7x2 + -7x3 + -1x4 + -12x + x5 = 12x + 7x2 + -7x3 + -1x4 + -12x + x5

Reorder the terms:
12x + -12x + 7x2 + -7x3 + -1x4 + x5 = 12x + 7x2 + -7x3 + -1x4 + -12x + x5

Combine like terms: 12x + -12x = 0
0 + 7x2 + -7x3 + -1x4 + x5 = 12x + 7x2 + -7x3 + -1x4 + -12x + x5
7x2 + -7x3 + -1x4 + x5 = 12x + 7x2 + -7x3 + -1x4 + -12x + x5

Reorder the terms:
7x2 + -7x3 + -1x4 + x5 = 12x + -12x + 7x2 + -7x3 + -1x4 + x5

Combine like terms: 12x + -12x = 0
7x2 + -7x3 + -1x4 + x5 = 0 + 7x2 + -7x3 + -1x4 + x5
7x2 + -7x3 + -1x4 + x5 = 7x2 + -7x3 + -1x4 + x5

Add '-7x2' to each side of the equation.
7x2 + -7x3 + -1x4 + -7x2 + x5 = 7x2 + -7x3 + -1x4 + -7x2 + x5

Reorder the terms:
7x2 + -7x2 + -7x3 + -1x4 + x5 = 7x2 + -7x3 + -1x4 + -7x2 + x5

Combine like terms: 7x2 + -7x2 = 0
0 + -7x3 + -1x4 + x5 = 7x2 + -7x3 + -1x4 + -7x2 + x5
-7x3 + -1x4 + x5 = 7x2 + -7x3 + -1x4 + -7x2 + x5

Reorder the terms:
-7x3 + -1x4 + x5 = 7x2 + -7x2 + -7x3 + -1x4 + x5

Combine like terms: 7x2 + -7x2 = 0
-7x3 + -1x4 + x5 = 0 + -7x3 + -1x4 + x5
-7x3 + -1x4 + x5 = -7x3 + -1x4 + x5

Add '7x3' to each side of the equation.
-7x3 + -1x4 + 7x3 + x5 = -7x3 + -1x4 + 7x3 + x5

Reorder the terms:
-7x3 + 7x3 + -1x4 + x5 = -7x3 + -1x4 + 7x3 + x5

Combine like terms: -7x3 + 7x3 = 0
0 + -1x4 + x5 = -7x3 + -1x4 + 7x3 + x5
-1x4 + x5 = -7x3 + -1x4 + 7x3 + x5

Reorder the terms:
-1x4 + x5 = -7x3 + 7x3 + -1x4 + x5

Combine like terms: -7x3 + 7x3 = 0
-1x4 + x5 = 0 + -1x4 + x5
-1x4 + x5 = -1x4 + x5

Add 'x4' to each side of the equation.
-1x4 + x4 + x5 = -1x4 + x4 + x5

Combine like terms: -1x4 + x4 = 0
0 + x5 = -1x4 + x4 + x5
x5 = -1x4 + x4 + x5

Combine like terms: -1x4 + x4 = 0
x5 = 0 + x5
x5 = x5

Add '-1x5' to each side of the equation.
x5 + -1x5 = x5 + -1x5

Combine like terms: x5 + -1x5 = 0
0 = x5 + -1x5

Combine like terms: x5 + -1x5 = 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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