60-60x=(8x+4)(x-1)

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Solution for 60-60x=(8x+4)(x-1) equation: 


Simplifying
60 + -60x = (8x + 4)(x + -1)

Reorder the terms:
60 + -60x = (4 + 8x)(x + -1)

Reorder the terms:
60 + -60x = (4 + 8x)(-1 + x)

Multiply (4 + 8x) * (-1 + x)
60 + -60x = (4(-1 + x) + 8x * (-1 + x))
60 + -60x = ((-1 * 4 + x * 4) + 8x * (-1 + x))
60 + -60x = ((-4 + 4x) + 8x * (-1 + x))
60 + -60x = (-4 + 4x + (-1 * 8x + x * 8x))
60 + -60x = (-4 + 4x + (-8x + 8x2))

Combine like terms: 4x + -8x = -4x
60 + -60x = (-4 + -4x + 8x2)

Solving
60 + -60x = -4 + -4x + 8x2

Solving for variable 'x'.

Reorder the terms:
60 + 4 + -60x + 4x + -8x2 = -4 + -4x + 8x2 + 4 + 4x + -8x2

Combine like terms: 60 + 4 = 64
64 + -60x + 4x + -8x2 = -4 + -4x + 8x2 + 4 + 4x + -8x2

Combine like terms: -60x + 4x = -56x
64 + -56x + -8x2 = -4 + -4x + 8x2 + 4 + 4x + -8x2

Reorder the terms:
64 + -56x + -8x2 = -4 + 4 + -4x + 4x + 8x2 + -8x2

Combine like terms: -4 + 4 = 0
64 + -56x + -8x2 = 0 + -4x + 4x + 8x2 + -8x2
64 + -56x + -8x2 = -4x + 4x + 8x2 + -8x2

Combine like terms: -4x + 4x = 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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