3(3x-1)(5x-1)=0

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Solution for 3(3x-1)(5x-1)=0 equation: 


Simplifying
3(3x + -1)(5x + -1) = 0

Reorder the terms:
3(-1 + 3x)(5x + -1) = 0

Reorder the terms:
3(-1 + 3x)(-1 + 5x) = 0

Multiply (-1 + 3x) * (-1 + 5x)
3(-1(-1 + 5x) + 3x * (-1 + 5x)) = 0
3((-1 * -1 + 5x * -1) + 3x * (-1 + 5x)) = 0
3((1 + -5x) + 3x * (-1 + 5x)) = 0
3(1 + -5x + (-1 * 3x + 5x * 3x)) = 0
3(1 + -5x + (-3x + 15x2)) = 0

Combine like terms: -5x + -3x = -8x
3(1 + -8x + 15x2) = 0
(1 * 3 + -8x * 3 + 15x2 * 3) = 0
(3 + -24x + 45x2) = 0

Solving
3 + -24x + 45x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(1 + -8x + 15x2) = 0

Factor a trinomial.
3((1 + -5x)(1 + -3x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(1 + -5x)' equal to zero and attempt to solve:

Simplifying
1 + -5x = 0

Solving
1 + -5x = 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 + -5x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -5x = 0 + -1
-5x = 0 + -1

Combine like terms: 0 + -1 = -1
-5x = -1

Divide each side by '-5'.
x = 0.2

Simplifying
x = 0.2

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 = {0.2, 0.3333333333}

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