(X^2-4x+6)(x^2+8x-1)=1

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Solution for (X^2-4x+6)(x^2+8x-1)=1 equation:


Simplifying
(X2 + -4x + 6)(x2 + 8x + -1) = 1

Reorder the terms:
(6 + X2 + -4x)(x2 + 8x + -1) = 1

Reorder the terms:
(6 + X2 + -4x)(-1 + 8x + x2) = 1

Multiply (6 + X2 + -4x) * (-1 + 8x + x2)
(6(-1 + 8x + x2) + X2(-1 + 8x + x2) + -4x * (-1 + 8x + x2)) = 1
((-1 * 6 + 8x * 6 + x2 * 6) + X2(-1 + 8x + x2) + -4x * (-1 + 8x + x2)) = 1
((-6 + 48x + 6x2) + X2(-1 + 8x + x2) + -4x * (-1 + 8x + x2)) = 1
(-6 + 48x + 6x2 + (-1 * X2 + 8x * X2 + x2 * X2) + -4x * (-1 + 8x + x2)) = 1
(-6 + 48x + 6x2 + (-1X2 + 8xX2 + x2X2) + -4x * (-1 + 8x + x2)) = 1
(-6 + 48x + 6x2 + -1X2 + 8xX2 + x2X2 + (-1 * -4x + 8x * -4x + x2 * -4x)) = 1
(-6 + 48x + 6x2 + -1X2 + 8xX2 + x2X2 + (4x + -32x2 + -4x3)) = 1

Reorder the terms:
(-6 + -1X2 + 48x + 4x + 8xX2 + 6x2 + -32x2 + x2X2 + -4x3) = 1

Combine like terms: 48x + 4x = 52x
(-6 + -1X2 + 52x + 8xX2 + 6x2 + -32x2 + x2X2 + -4x3) = 1

Combine like terms: 6x2 + -32x2 = -26x2
(-6 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3) = 1

Solving
-6 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 1

Solving for variable 'X'.

Move all terms containing X to the left, all other terms to the right.

Add '6' to each side of the equation.
-6 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + 6 + -4x3 = 1 + 6

Reorder the terms:
-6 + 6 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 1 + 6

Combine like terms: -6 + 6 = 0
0 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 1 + 6
-1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 1 + 6

Combine like terms: 1 + 6 = 7
-1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 7

Add '-52x' to each side of the equation.
-1X2 + 52x + 8xX2 + -26x2 + x2X2 + -52x + -4x3 = 7 + -52x

Reorder the terms:
-1X2 + 52x + -52x + 8xX2 + -26x2 + x2X2 + -4x3 = 7 + -52x

Combine like terms: 52x + -52x = 0
-1X2 + 0 + 8xX2 + -26x2 + x2X2 + -4x3 = 7 + -52x
-1X2 + 8xX2 + -26x2 + x2X2 + -4x3 = 7 + -52x

Add '26x2' to each side of the equation.
-1X2 + 8xX2 + -26x2 + x2X2 + 26x2 + -4x3 = 7 + -52x + 26x2

Reorder the terms:
-1X2 + 8xX2 + -26x2 + 26x2 + x2X2 + -4x3 = 7 + -52x + 26x2

Combine like terms: -26x2 + 26x2 = 0
-1X2 + 8xX2 + 0 + x2X2 + -4x3 = 7 + -52x + 26x2
-1X2 + 8xX2 + x2X2 + -4x3 = 7 + -52x + 26x2

Add '4x3' to each side of the equation.
-1X2 + 8xX2 + x2X2 + -4x3 + 4x3 = 7 + -52x + 26x2 + 4x3

Combine like terms: -4x3 + 4x3 = 0
-1X2 + 8xX2 + x2X2 + 0 = 7 + -52x + 26x2 + 4x3
-1X2 + 8xX2 + x2X2 = 7 + -52x + 26x2 + 4x3

Reorder the terms:
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 7 + -52x + 26x2 + 4x3 + -7 + 52x + -26x2 + -4x3

Reorder the terms:
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 7 + -7 + -52x + 52x + 26x2 + -26x2 + 4x3 + -4x3

Combine like terms: 7 + -7 = 0
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 0 + -52x + 52x + 26x2 + -26x2 + 4x3 + -4x3
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = -52x + 52x + 26x2 + -26x2 + 4x3 + -4x3

Combine like terms: -52x + 52x = 0
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 0 + 26x2 + -26x2 + 4x3 + -4x3
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 26x2 + -26x2 + 4x3 + -4x3

Combine like terms: 26x2 + -26x2 = 0
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 0 + 4x3 + -4x3
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 4x3 + -4x3

Combine like terms: 4x3 + -4x3 = 0
-7 + -1X2 + 52x + 8xX2 + -26x2 + x2X2 + -4x3 = 0

The solution to this equation could not be determined.

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