(3x-1)(x+1)=4

Solution for (3x-1)(x+1)=4 equation:

Simplifying
(3x + -1)(x + 1) = 4

Reorder the terms:
(-1 + 3x)(x + 1) = 4

Reorder the terms:
(-1 + 3x)(1 + x) = 4

Multiply (-1 + 3x) * (1 + x)
(-1(1 + x) + 3x * (1 + x)) = 4
((1 * -1 + x * -1) + 3x * (1 + x)) = 4
((-1 + -1x) + 3x * (1 + x)) = 4
(-1 + -1x + (1 * 3x + x * 3x)) = 4
(-1 + -1x + (3x + 3x2)) = 4

Combine like terms: -1x + 3x = 2x
(-1 + 2x + 3x2) = 4

Solving
-1 + 2x + 3x2 = 4

Solving for variable 'x'.

Reorder the terms:
-1 + -4 + 2x + 3x2 = 4 + -4

Combine like terms: -1 + -4 = -5
-5 + 2x + 3x2 = 4 + -4

Combine like terms: 4 + -4 = 0
-5 + 2x + 3x2 = 0

Factor a trinomial.
(-5 + -3x)(1 + -1x) = 0

Subproblem 1
Set the factor '(-5 + -3x)' equal to zero and attempt to solve:

Simplifying
-5 + -3x = 0

Solving
-5 + -3x = 0

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

Add '5' to each side of the equation.
-5 + 5 + -3x = 0 + 5

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

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

Divide each side by '-3'.
x = -1.666666667

Simplifying
x = -1.666666667
Subproblem 2
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
Solution
x = {-1.666666667, 1}