63-63x=(8x+1)(x-1)

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Solution for 63-63x=(8x+1)(x-1) equation:


Simplifying
63 + -63x = (8x + 1)(x + -1)

Reorder the terms:
63 + -63x = (1 + 8x)(x + -1)

Reorder the terms:
63 + -63x = (1 + 8x)(-1 + x)

Multiply (1 + 8x) * (-1 + x)
63 + -63x = (1(-1 + x) + 8x * (-1 + x))
63 + -63x = ((-1 * 1 + x * 1) + 8x * (-1 + x))
63 + -63x = ((-1 + 1x) + 8x * (-1 + x))
63 + -63x = (-1 + 1x + (-1 * 8x + x * 8x))
63 + -63x = (-1 + 1x + (-8x + 8x2))

Combine like terms: 1x + -8x = -7x
63 + -63x = (-1 + -7x + 8x2)

Solving
63 + -63x = -1 + -7x + 8x2

Solving for variable 'x'.

Reorder the terms:
63 + 1 + -63x + 7x + -8x2 = -1 + -7x + 8x2 + 1 + 7x + -8x2

Combine like terms: 63 + 1 = 64
64 + -63x + 7x + -8x2 = -1 + -7x + 8x2 + 1 + 7x + -8x2

Combine like terms: -63x + 7x = -56x
64 + -56x + -8x2 = -1 + -7x + 8x2 + 1 + 7x + -8x2

Reorder the terms:
64 + -56x + -8x2 = -1 + 1 + -7x + 7x + 8x2 + -8x2

Combine like terms: -1 + 1 = 0
64 + -56x + -8x2 = 0 + -7x + 7x + 8x2 + -8x2
64 + -56x + -8x2 = -7x + 7x + 8x2 + -8x2

Combine like terms: -7x + 7x = 0
64 + -56x + -8x2 = 0 + 8x2 + -8x2
64 + -56x + -8x2 = 8x2 + -8x2

Combine like terms: 8x2 + -8x2 = 0
64 + -56x + -8x2 = 0

Factor out the Greatest Common Factor (GCF), '8'.
8(8 + -7x + -1x2) = 0

Factor a trinomial.
8((1 + -1x)(8 + x)) = 0

Ignore the factor 8.

Subproblem 1

Set the factor '(1 + -1x)' equal to zero and attempt to solve: Simplifying 1 + -1x = 0 Solving 1 + -1x = 0 Move all terms containing x to the left, all other terms to the right. Add '-1' to each side of the equation. 1 + -1 + -1x = 0 + -1 Combine like terms: 1 + -1 = 0 0 + -1x = 0 + -1 -1x = 0 + -1 Combine like terms: 0 + -1 = -1 -1x = -1 Divide each side by '-1'. x = 1 Simplifying x = 1

Subproblem 2

Set the factor '(8 + x)' equal to zero and attempt to solve: Simplifying 8 + x = 0 Solving 8 + x = 0 Move all terms containing x to the left, all other terms to the right. Add '-8' to each side of the equation. 8 + -8 + x = 0 + -8 Combine like terms: 8 + -8 = 0 0 + x = 0 + -8 x = 0 + -8 Combine like terms: 0 + -8 = -8 x = -8 Simplifying x = -8

Solution

x = {1, -8}

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