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

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


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

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

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

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

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

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

Solving for variable 'x'.

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

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

Combine like terms: 7 + -7 = 0
-8 + -2x + 3x2 = 0

Factor a trinomial.
(-4 + -3x)(2 + -1x) = 0


Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

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

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 2}

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