2(x-1)(3x+1)=0

Solution for 2(x-1)(3x+1)=0 equation:

Simplifying
2(x + -1)(3x + 1) = 0

Reorder the terms:
2(-1 + x)(3x + 1) = 0

Reorder the terms:
2(-1 + x)(1 + 3x) = 0

Multiply (-1 + x) * (1 + 3x)
2(-1(1 + 3x) + x(1 + 3x)) = 0
2((1 * -1 + 3x * -1) + x(1 + 3x)) = 0
2((-1 + -3x) + x(1 + 3x)) = 0
2(-1 + -3x + (1 * x + 3x * x)) = 0
2(-1 + -3x + (1x + 3x2)) = 0

Combine like terms: -3x + 1x = -2x
2(-1 + -2x + 3x2) = 0
(-1 * 2 + -2x * 2 + 3x2 * 2) = 0
(-2 + -4x + 6x2) = 0

Solving
-2 + -4x + 6x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -3x)' equal to zero and attempt to solve:

Simplifying
-1 + -3x = 0

Solving
-1 + -3x = 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 + -3x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3x = 0 + 1
-3x = 0 + 1

Combine like terms: 0 + 1 = 1
-3x = 1

Divide each side by '-3'.
x = -0.3333333333

Simplifying
x = -0.3333333333
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 = {-0.3333333333, 1}