(3x-1)(2x+6)=0

Solution for (3x-1)(2x+6)=0 equation:

Simplifying
(3x + -1)(2x + 6) = 0

Reorder the terms:
(-1 + 3x)(2x + 6) = 0

Reorder the terms:
(-1 + 3x)(6 + 2x) = 0

Multiply (-1 + 3x) * (6 + 2x)
(-1(6 + 2x) + 3x * (6 + 2x)) = 0
((6 * -1 + 2x * -1) + 3x * (6 + 2x)) = 0
((-6 + -2x) + 3x * (6 + 2x)) = 0
(-6 + -2x + (6 * 3x + 2x * 3x)) = 0
(-6 + -2x + (18x + 6x2)) = 0

Combine like terms: -2x + 18x = 16x
(-6 + 16x + 6x2) = 0

Solving
-6 + 16x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + 8x + 3x2) = 0

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

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

Simplifying
-3 + -1x = 0

Solving
-3 + -1x = 0

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

Add '3' to each side of the equation.
-3 + 3 + -1x = 0 + 3

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

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

Divide each side by '-1'.
x = -3

Simplifying
x = -3
Subproblem 2
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
Solution
x = {-3, 0.3333333333}