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

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

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

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

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

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

Combine like terms: -2x + -18x = -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}