(3x-1)(2x-5)=0

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Solution for (3x-1)(2x-5)=0 equation: 


Simplifying
(3x + -1)(2x + -5) = 0

Reorder the terms:
(-1 + 3x)(2x + -5) = 0

Reorder the terms:
(-1 + 3x)(-5 + 2x) = 0

Multiply (-1 + 3x) * (-5 + 2x)
(-1(-5 + 2x) + 3x * (-5 + 2x)) = 0
((-5 * -1 + 2x * -1) + 3x * (-5 + 2x)) = 0
((5 + -2x) + 3x * (-5 + 2x)) = 0
(5 + -2x + (-5 * 3x + 2x * 3x)) = 0
(5 + -2x + (-15x + 6x2)) = 0

Combine like terms: -2x + -15x = -17x
(5 + -17x + 6x2) = 0

Solving
5 + -17x + 6x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(1 + -3x)(5 + -2x) = 0


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 '(5 + -2x)' equal to zero and attempt to solve:

Simplifying
5 + -2x = 0

Solving
5 + -2x = 0

Move all terms containing x to the left, all other terms to the right.

Add '-5' to each side of the equation.
5 + -5 + -2x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -2x = 0 + -5
-2x = 0 + -5

Combine like terms: 0 + -5 = -5
-2x = -5

Divide each side by '-2'.
x = 2.5

Simplifying
x = 2.5
Solution
x = {0.3333333333, 2.5}

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