(x-5)(x-1)(x^2+5x+25)(x^2+x+1)=x^6-126x^3+125

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Solution for (x-5)(x-1)(x^2+5x+25)(x^2+x+1)=x^6-126x^3+125 equation: 


Simplifying
(x + -5)(x + -1)(x2 + 5x + 25)(x2 + x + 1) = x6 + -126x3 + 125

Reorder the terms:
(-5 + x)(x + -1)(x2 + 5x + 25)(x2 + x + 1) = x6 + -126x3 + 125

Reorder the terms:
(-5 + x)(-1 + x)(x2 + 5x + 25)(x2 + x + 1) = x6 + -126x3 + 125

Reorder the terms:
(-5 + x)(-1 + x)(25 + 5x + x2)(x2 + x + 1) = x6 + -126x3 + 125

Reorder the terms:
(-5 + x)(-1 + x)(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125

Multiply (-5 + x) * (-1 + x)
(-5(-1 + x) + x(-1 + x))(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125
((-1 * -5 + x * -5) + x(-1 + x))(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125
((5 + -5x) + x(-1 + x))(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125
(5 + -5x + (-1 * x + x * x))(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125
(5 + -5x + (-1x + x2))(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125

Combine like terms: -5x + -1x = -6x
(5 + -6x + x2)(25 + 5x + x2)(1 + x + x2) = x6 + -126x3 + 125

Multiply (5 + -6x + x2) * (25 + 5x + x2)
(5(25 + 5x + x2) + -6x * (25 + 5x + x2) + x2(25 + 5x + x2))(1 + x + x2) = x6 + -126x3 + 125
((25 * 5 + 5x * 5 + x2 * 5) + -6x * (25 + 5x + x2) + x2(25 + 5x + x2))(1 + x + x2) = x6 + -126x3 + 125
((125 + 25x + 5x2) + -6x * (25 + 5x + x2) + x2(25 + 5x + x2))(1 + x + x2) = x6 + -126x3 + 125
(125 + 25x + 5x2 + (25 * -6x + 5x * -6x + x2 * -6x) + x2(25 + 5x + x2))(1 + x + x2) = x6 + -126x3 + 125
(125 + 25x + 5x2 + (-150x + -30x2 + -6x3) + x2(25 + 5x + x2))(1 + x + x2) = x6 + -126x3 + 125
(125 + 25x + 5x2 + -150x + -30x2 + -6x3 + (25 * x2 + 5x * x2 + x2 * x2))(1 + x + x2) = x6 + -126x3 + 125
(125 + 25x + 5x2 + -150x + -30x2 + -6x3 + (25x2 + 5x3 + x4))(1 + x + x2) = x6 + -126x3 + 125

Reorder the terms:
(125 + 25x + -150x + 5x2 + -30x2 + 25x2 + -6x3 + 5x3 + x4)(1 + x + x2) = x6 + -126x3 + 125

Combine like terms: 25x + -150x = -125x
(125 + -125x + 5x2 + -30x2 + 25x2 + -6x3 + 5x3 + x4)(1 + x + x2) = x6 + -126x3 + 125

Combine like terms: 5x2 + -30x2 = -25x2
(125 + -125x + -25x2 + 25x2 + -6x3 + 5x3 + x4)(1 + x + x2) = x6 + -126x3 + 125

Combine like terms: -25x2 + 25x2 = 0
(125 + -125x + 0 + -6x3 + 5x3 + x4)(1 + x + x2) = x6 + -126x3 + 125
(125 + -125x + -6x3 + 5x3 + x4)(1 + x + x2) = x6 + -126x3 + 125

Combine like terms: -6x3 + 5x3 = -1x3
(125 + -125x + -1x3 + x4)(1 + x + x2) = x6 + -126x3 + 125

Multiply (125 + -125x + -1x3 + x4) * (1 + x + x2)
(125(1 + x + x2) + -125x * (1 + x + x2) + -1x3 * (1 + x + x2) + x4(1 + x + x2)) = x6 + -126x3 + 125
((1 * 125 + x * 125 + x2 * 125) + -125x * (1 + x + x2) + -1x3 * (1 + x + x2) + x4(1 + x + x2)) = x6 + -126x3 + 125
((125 + 125x + 125x2) + -125x * (1 + x + x2) + -1x3 * (1 + x + x2) + x4(1 + x + x2)) = x6 + -126x3 + 125
(125 + 125x + 125x2 + (1 * -125x + x * -125x + x2 * -125x) + -1x3 * (1 + x + x2) + x4(1 + x + x2)) = x6 + -126x3 + 125
(125 + 125x + 125x2 + (-125x + -125x2 + -125x3) + -1x3 * (1 + x + x2) + x4(1 + x + x2)) = x6 + -126x3 + 125
(125 + 125x + 125x2 + -125x + -125x2 + -125x3 + (1 * -1x3 + x * -1x3 + x2 * -1x3) + x4(1 + x + x2)) = x6 + -126x3 + 125
(125 + 125x + 125x2 + -125x + -125x2 + -125x3 + (-1x3 + -1x4 + -1x5) + x4(1 + x + x2)) = x6 + -126x3 + 125
(125 + 125x + 125x2 + -125x + -125x2 + -125x3 + -1x3 + -1x4 + -1x5 + (1 * x4 + x * x4 + x2 * x4)) = x6 + -126x3 + 125
(125 + 125x + 125x2 + -125x + -125x2 + -125x3 + -1x3 + -1x4 + -1x5 + (1x4 + x5 + x6)) = x6 + -126x3 + 125

Reorder the terms:
(125 + 125x + -125x + 125x2 + -125x2 + -125x3 + -1x3 + -1x4 + 1x4 + -1x5 + x5 + x6) = x6 + -126x3 + 125

Combine like terms: 125x + -125x = 0
(125 + 0 + 125x2 + -125x2 + -125x3 + -1x3 + -1x4 + 1x4 + -1x5 + x5 + x6) = x6 + -126x3 + 125
(125 + 125x2 + -125x2 + -125x3 + -1x3 + -1x4 + 1x4 + -1x5 + x5 + x6) = x6 + -126x3 + 125

Combine like terms: 125x2 + -125x2 = 0
(125 + 0 + -125x3 + -1x3 + -1x4 + 1x4 + -1x5 + x5 + x6) = x6 + -126x3 + 125
(125 + -125x3 + -1x3 + -1x4 + 1x4 + -1x5 + x5 + x6) = x6 + -126x3 + 125

Combine like terms: -125x3 + -1x3 = -126x3
(125 + -126x3 + -1x4 + 1x4 + -1x5 + x5 + x6) = x6 + -126x3 + 125

Combine like terms: -1x4 + 1x4 = 0
(125 + -126x3 + 0 + -1x5 + x5 + x6) = x6 + -126x3 + 125
(125 + -126x3 + -1x5 + x5 + x6) = x6 + -126x3 + 125

Combine like terms: -1x5 + x5 = 0
(125 + -126x3 + 0 + x6) = x6 + -126x3 + 125
(125 + -126x3 + x6) = x6 + -126x3 + 125

Reorder the terms:
125 + -126x3 + x6 = 125 + -126x3 + x6

Add '-125' to each side of the equation.
125 + -126x3 + -125 + x6 = 125 + -126x3 + -125 + x6

Reorder the terms:
125 + -125 + -126x3 + x6 = 125 + -126x3 + -125 + x6

Combine like terms: 125 + -125 = 0
0 + -126x3 + x6 = 125 + -126x3 + -125 + x6
-126x3 + x6 = 125 + -126x3 + -125 + x6

Reorder the terms:
-126x3 + x6 = 125 + -125 + -126x3 + x6

Combine like terms: 125 + -125 = 0
-126x3 + x6 = 0 + -126x3 + x6
-126x3 + x6 = -126x3 + x6

Add '126x3' to each side of the equation.
-126x3 + 126x3 + x6 = -126x3 + 126x3 + x6

Combine like terms: -126x3 + 126x3 = 0
0 + x6 = -126x3 + 126x3 + x6
x6 = -126x3 + 126x3 + x6

Combine like terms: -126x3 + 126x3 = 0
x6 = 0 + x6
x6 = x6

Add '-1x6' to each side of the equation.
x6 + -1x6 = x6 + -1x6

Combine like terms: x6 + -1x6 = 0
0 = x6 + -1x6

Combine like terms: x6 + -1x6 = 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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