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

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


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

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

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

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

Combine like terms: -3x + -6x = -9x
(1 + -9x + 18x2) = 0

Solving
1 + -9x + 18x2 = 0

Solving for variable 'x'.

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


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 '(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 = {0.1666666667, 0.3333333333}

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