48(1-x)=(7x-1)(x-1)

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Solution for 48(1-x)=(7x-1)(x-1) equation: 


Simplifying
48(1 + -1x) = (7x + -1)(x + -1)
(1 * 48 + -1x * 48) = (7x + -1)(x + -1)
(48 + -48x) = (7x + -1)(x + -1)

Reorder the terms:
48 + -48x = (-1 + 7x)(x + -1)

Reorder the terms:
48 + -48x = (-1 + 7x)(-1 + x)

Multiply (-1 + 7x) * (-1 + x)
48 + -48x = (-1(-1 + x) + 7x * (-1 + x))
48 + -48x = ((-1 * -1 + x * -1) + 7x * (-1 + x))
48 + -48x = ((1 + -1x) + 7x * (-1 + x))
48 + -48x = (1 + -1x + (-1 * 7x + x * 7x))
48 + -48x = (1 + -1x + (-7x + 7x2))

Combine like terms: -1x + -7x = -8x
48 + -48x = (1 + -8x + 7x2)

Solving
48 + -48x = 1 + -8x + 7x2

Solving for variable 'x'.

Reorder the terms:
48 + -1 + -48x + 8x + -7x2 = 1 + -8x + 7x2 + -1 + 8x + -7x2

Combine like terms: 48 + -1 = 47
47 + -48x + 8x + -7x2 = 1 + -8x + 7x2 + -1 + 8x + -7x2

Combine like terms: -48x + 8x = -40x
47 + -40x + -7x2 = 1 + -8x + 7x2 + -1 + 8x + -7x2

Reorder the terms:
47 + -40x + -7x2 = 1 + -1 + -8x + 8x + 7x2 + -7x2

Combine like terms: 1 + -1 = 0
47 + -40x + -7x2 = 0 + -8x + 8x + 7x2 + -7x2
47 + -40x + -7x2 = -8x + 8x + 7x2 + -7x2

Combine like terms: -8x + 8x = 0
47 + -40x + -7x2 = 0 + 7x2 + -7x2
47 + -40x + -7x2 = 7x2 + -7x2

Combine like terms: 7x2 + -7x2 = 0
47 + -40x + -7x2 = 0

Factor a trinomial.
(1 + -1x)(47 + 7x) = 0


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 '(47 + 7x)' equal to zero and attempt to solve:

Simplifying
47 + 7x = 0

Solving
47 + 7x = 0

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

Add '-47' to each side of the equation.
47 + -47 + 7x = 0 + -47

Combine like terms: 47 + -47 = 0
0 + 7x = 0 + -47
7x = 0 + -47

Combine like terms: 0 + -47 = -47
7x = -47

Divide each side by '7'.
x = -6.714285714

Simplifying
x = -6.714285714
Solution
x = {1, -6.714285714}

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