7-7x=(3x+2)(x-1)

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Solution for 7-7x=(3x+2)(x-1) equation: 


Simplifying
7 + -7x = (3x + 2)(x + -1)

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

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

Multiply (2 + 3x) * (-1 + x)
7 + -7x = (2(-1 + x) + 3x * (-1 + x))
7 + -7x = ((-1 * 2 + x * 2) + 3x * (-1 + x))
7 + -7x = ((-2 + 2x) + 3x * (-1 + x))
7 + -7x = (-2 + 2x + (-1 * 3x + x * 3x))
7 + -7x = (-2 + 2x + (-3x + 3x2))

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

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

Solving for variable 'x'.

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

Combine like terms: 7 + 2 = 9
9 + -7x + x + -3x2 = -2 + -1x + 3x2 + 2 + x + -3x2

Combine like terms: -7x + x = -6x
9 + -6x + -3x2 = -2 + -1x + 3x2 + 2 + x + -3x2

Reorder the terms:
9 + -6x + -3x2 = -2 + 2 + -1x + x + 3x2 + -3x2

Combine like terms: -2 + 2 = 0
9 + -6x + -3x2 = 0 + -1x + x + 3x2 + -3x2
9 + -6x + -3x2 = -1x + x + 3x2 + -3x2

Combine like terms: -1x + x = 0
9 + -6x + -3x2 = 0 + 3x2 + -3x2
9 + -6x + -3x2 = 3x2 + -3x2

Combine like terms: 3x2 + -3x2 = 0
9 + -6x + -3x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + -2x + -1x2) = 0

Factor a trinomial.
3((1 + -1x)(3 + x)) = 0

Ignore the factor 3.

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

Simplifying
3 + x = 0

Solving
3 + x = 0

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

Add '-3' to each side of the equation.
3 + -3 + x = 0 + -3

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

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

Simplifying
x = -3
Solution
x = {1, -3}

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