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

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

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

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

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

Multiply (1 + 6x) * (-6 + 2x)
(1(-6 + 2x) + 6x * (-6 + 2x)) = 0
((-6 * 1 + 2x * 1) + 6x * (-6 + 2x)) = 0
((-6 + 2x) + 6x * (-6 + 2x)) = 0
(-6 + 2x + (-6 * 6x + 2x * 6x)) = 0
(-6 + 2x + (-36x + 12x2)) = 0

Combine like terms: 2x + -36x = -34x
(-6 + -34x + 12x2) = 0

Solving
-6 + -34x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-3 + -17x + 6x2) = 0

Factor a trinomial.
2((-1 + -6x)(3 + -1x)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(-1 + -6x)' equal to zero and attempt to solve:

Simplifying
-1 + -6x = 0

Solving
-1 + -6x = 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 + -6x = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -6x = 0 + 1
-6x = 0 + 1

Combine like terms: 0 + 1 = 1
-6x = 1

Divide each side by '-6'.
x = -0.1666666667

Simplifying
x = -0.1666666667
Subproblem 2
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
Solution
x = {-0.1666666667, 3}