7-7x=(3x+1)(x-1)

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Solution for 7-7x=(3x+1)(x-1) equation: 


Simplifying
7 + -7x = (3x + 1)(x + -1)

Reorder the terms:
7 + -7x = (1 + 3x)(x + -1)

Reorder the terms:
7 + -7x = (1 + 3x)(-1 + x)

Multiply (1 + 3x) * (-1 + x)
7 + -7x = (1(-1 + x) + 3x * (-1 + x))
7 + -7x = ((-1 * 1 + x * 1) + 3x * (-1 + x))
7 + -7x = ((-1 + 1x) + 3x * (-1 + x))
7 + -7x = (-1 + 1x + (-1 * 3x + x * 3x))
7 + -7x = (-1 + 1x + (-3x + 3x2))

Combine like terms: 1x + -3x = -2x
7 + -7x = (-1 + -2x + 3x2)

Solving
7 + -7x = -1 + -2x + 3x2

Solving for variable 'x'.

Reorder the terms:
7 + 1 + -7x + 2x + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: 7 + 1 = 8
8 + -7x + 2x + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Combine like terms: -7x + 2x = -5x
8 + -5x + -3x2 = -1 + -2x + 3x2 + 1 + 2x + -3x2

Reorder the terms:
8 + -5x + -3x2 = -1 + 1 + -2x + 2x + 3x2 + -3x2

Combine like terms: -1 + 1 = 0
8 + -5x + -3x2 = 0 + -2x + 2x + 3x2 + -3x2
8 + -5x + -3x2 = -2x + 2x + 3x2 + -3x2

Combine like terms: -2x + 2x = 0
8 + -5x + -3x2 = 0 + 3x2 + -3x2
8 + -5x + -3x2 = 3x2 + -3x2

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

Factor a trinomial.
(1 + -1x)(8 + 3x) = 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 '(8 + 3x)' equal to zero and attempt to solve:

Simplifying
8 + 3x = 0

Solving
8 + 3x = 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 + 3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + 3x = 0 + -8
3x = 0 + -8

Combine like terms: 0 + -8 = -8
3x = -8

Divide each side by '3'.
x = -2.666666667

Simplifying
x = -2.666666667
Solution
x = {1, -2.666666667}

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