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

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

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

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

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

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

Combine like terms: -18x + -2x = -20x
(6 + -20x + 6x2) = 0

Solving
6 + -20x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(3 + -10x + 3x2) = 0

Factor a trinomial.
2((1 + -3x)(3 + -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 '(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 = {0.3333333333, 3}