62-62X=(8X+2)(X-1)

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Solution for 62-62X=(8X+2)(X-1) equation: 


Simplifying
62 + -62X = (8X + 2)(X + -1)

Reorder the terms:
62 + -62X = (2 + 8X)(X + -1)

Reorder the terms:
62 + -62X = (2 + 8X)(-1 + X)

Multiply (2 + 8X) * (-1 + X)
62 + -62X = (2(-1 + X) + 8X * (-1 + X))
62 + -62X = ((-1 * 2 + X * 2) + 8X * (-1 + X))
62 + -62X = ((-2 + 2X) + 8X * (-1 + X))
62 + -62X = (-2 + 2X + (-1 * 8X + X * 8X))
62 + -62X = (-2 + 2X + (-8X + 8X2))

Combine like terms: 2X + -8X = -6X
62 + -62X = (-2 + -6X + 8X2)

Solving
62 + -62X = -2 + -6X + 8X2

Solving for variable 'X'.

Reorder the terms:
62 + 2 + -62X + 6X + -8X2 = -2 + -6X + 8X2 + 2 + 6X + -8X2

Combine like terms: 62 + 2 = 64
64 + -62X + 6X + -8X2 = -2 + -6X + 8X2 + 2 + 6X + -8X2

Combine like terms: -62X + 6X = -56X
64 + -56X + -8X2 = -2 + -6X + 8X2 + 2 + 6X + -8X2

Reorder the terms:
64 + -56X + -8X2 = -2 + 2 + -6X + 6X + 8X2 + -8X2

Combine like terms: -2 + 2 = 0
64 + -56X + -8X2 = 0 + -6X + 6X + 8X2 + -8X2
64 + -56X + -8X2 = -6X + 6X + 8X2 + -8X2

Combine like terms: -6X + 6X = 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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