61-61x=(8x+3)(x-1)

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Solution for 61-61x=(8x+3)(x-1) equation: 


Simplifying
61 + -61x = (8x + 3)(x + -1)

Reorder the terms:
61 + -61x = (3 + 8x)(x + -1)

Reorder the terms:
61 + -61x = (3 + 8x)(-1 + x)

Multiply (3 + 8x) * (-1 + x)
61 + -61x = (3(-1 + x) + 8x * (-1 + x))
61 + -61x = ((-1 * 3 + x * 3) + 8x * (-1 + x))
61 + -61x = ((-3 + 3x) + 8x * (-1 + x))
61 + -61x = (-3 + 3x + (-1 * 8x + x * 8x))
61 + -61x = (-3 + 3x + (-8x + 8x2))

Combine like terms: 3x + -8x = -5x
61 + -61x = (-3 + -5x + 8x2)

Solving
61 + -61x = -3 + -5x + 8x2

Solving for variable 'x'.

Reorder the terms:
61 + 3 + -61x + 5x + -8x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Combine like terms: 61 + 3 = 64
64 + -61x + 5x + -8x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Combine like terms: -61x + 5x = -56x
64 + -56x + -8x2 = -3 + -5x + 8x2 + 3 + 5x + -8x2

Reorder the terms:
64 + -56x + -8x2 = -3 + 3 + -5x + 5x + 8x2 + -8x2

Combine like terms: -3 + 3 = 0
64 + -56x + -8x2 = 0 + -5x + 5x + 8x2 + -8x2
64 + -56x + -8x2 = -5x + 5x + 8x2 + -8x2

Combine like terms: -5x + 5x = 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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