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

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

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

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

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

Multiply (-2 + x) * (1 + 3x)
(-2(1 + 3x) + x(1 + 3x)) = 0
((1 * -2 + 3x * -2) + x(1 + 3x)) = 0
((-2 + -6x) + x(1 + 3x)) = 0
(-2 + -6x + (1 * x + 3x * x)) = 0
(-2 + -6x + (1x + 3x2)) = 0

Combine like terms: -6x + 1x = -5x
(-2 + -5x + 3x2) = 0

Solving
-2 + -5x + 3x2 = 0

Solving for variable 'x'.

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

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 '(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 = {-0.3333333333, 2}