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

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


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

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

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

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

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

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

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

Solving for variable 'x'.

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

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

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

Reorder the terms:
6 + -9x + 3x2 = -7 + 7 + 7x + -7x

Combine like terms: -7 + 7 = 0
6 + -9x + 3x2 = 0 + 7x + -7x
6 + -9x + 3x2 = 7x + -7x

Combine like terms: 7x + -7x = 0
6 + -9x + 3x2 = 0

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

Factor a trinomial.
3((1 + -1x)(2 + -1x)) = 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 '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {1, 2}

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