47-47x=(7x+2)(x-1)

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Solution for 47-47x=(7x+2)(x-1) equation: 


Simplifying
47 + -47x = (7x + 2)(x + -1)

Reorder the terms:
47 + -47x = (2 + 7x)(x + -1)

Reorder the terms:
47 + -47x = (2 + 7x)(-1 + x)

Multiply (2 + 7x) * (-1 + x)
47 + -47x = (2(-1 + x) + 7x * (-1 + x))
47 + -47x = ((-1 * 2 + x * 2) + 7x * (-1 + x))
47 + -47x = ((-2 + 2x) + 7x * (-1 + x))
47 + -47x = (-2 + 2x + (-1 * 7x + x * 7x))
47 + -47x = (-2 + 2x + (-7x + 7x2))

Combine like terms: 2x + -7x = -5x
47 + -47x = (-2 + -5x + 7x2)

Solving
47 + -47x = -2 + -5x + 7x2

Solving for variable 'x'.

Reorder the terms:
47 + 2 + -47x + 5x + -7x2 = -2 + -5x + 7x2 + 2 + 5x + -7x2

Combine like terms: 47 + 2 = 49
49 + -47x + 5x + -7x2 = -2 + -5x + 7x2 + 2 + 5x + -7x2

Combine like terms: -47x + 5x = -42x
49 + -42x + -7x2 = -2 + -5x + 7x2 + 2 + 5x + -7x2

Reorder the terms:
49 + -42x + -7x2 = -2 + 2 + -5x + 5x + 7x2 + -7x2

Combine like terms: -2 + 2 = 0
49 + -42x + -7x2 = 0 + -5x + 5x + 7x2 + -7x2
49 + -42x + -7x2 = -5x + 5x + 7x2 + -7x2

Combine like terms: -5x + 5x = 0
49 + -42x + -7x2 = 0 + 7x2 + -7x2
49 + -42x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
49 + -42x + -7x2 = 0

Factor out the Greatest Common Factor (GCF), '7'.
7(7 + -6x + -1x2) = 0

Factor a trinomial.
7((1 + -1x)(7 + x)) = 0

Ignore the factor 7.

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 '(7 + x)' equal to zero and attempt to solve:

Simplifying
7 + x = 0

Solving
7 + x = 0

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

Add '-7' to each side of the equation.
7 + -7 + x = 0 + -7

Combine like terms: 7 + -7 = 0
0 + x = 0 + -7
x = 0 + -7

Combine like terms: 0 + -7 = -7
x = -7

Simplifying
x = -7
Solution
x = {1, -7}

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