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

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

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

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

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

Multiply (-5 + x) * (-3 + 2x)
0 = 3(-5(-3 + 2x) + x(-3 + 2x))
0 = 3((-3 * -5 + 2x * -5) + x(-3 + 2x))
0 = 3((15 + -10x) + x(-3 + 2x))
0 = 3(15 + -10x + (-3 * x + 2x * x))
0 = 3(15 + -10x + (-3x + 2x2))

Combine like terms: -10x + -3x = -13x
0 = 3(15 + -13x + 2x2)
0 = (15 * 3 + -13x * 3 + 2x2 * 3)
0 = (45 + -39x + 6x2)

Solving
0 = 45 + -39x + 6x2

Solving for variable 'x'.

Combine like terms: 0 + -45 = -45
-45 + 39x + -6x2 = 45 + -39x + 6x2 + -45 + 39x + -6x2

Reorder the terms:
-45 + 39x + -6x2 = 45 + -45 + -39x + 39x + 6x2 + -6x2

Combine like terms: 45 + -45 = 0
-45 + 39x + -6x2 = 0 + -39x + 39x + 6x2 + -6x2
-45 + 39x + -6x2 = -39x + 39x + 6x2 + -6x2

Combine like terms: -39x + 39x = 0
-45 + 39x + -6x2 = 0 + 6x2 + -6x2
-45 + 39x + -6x2 = 6x2 + -6x2

Combine like terms: 6x2 + -6x2 = 0
-45 + 39x + -6x2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-15 + 13x + -2x2) = 0

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

Ignore the factor 3.
Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

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

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

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

Simplifying
x = 5
Subproblem 2
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {5, 1.5}