3(3x-4)(x-5)=0

Solution for 3(3x-4)(x-5)=0 equation:

Simplifying
3(3x + -4)(x + -5) = 0

Reorder the terms:
3(-4 + 3x)(x + -5) = 0

Reorder the terms:
3(-4 + 3x)(-5 + x) = 0

Multiply (-4 + 3x) * (-5 + x)
3(-4(-5 + x) + 3x * (-5 + x)) = 0
3((-5 * -4 + x * -4) + 3x * (-5 + x)) = 0
3((20 + -4x) + 3x * (-5 + x)) = 0
3(20 + -4x + (-5 * 3x + x * 3x)) = 0
3(20 + -4x + (-15x + 3x2)) = 0

Combine like terms: -4x + -15x = -19x
3(20 + -19x + 3x2) = 0
(20 * 3 + -19x * 3 + 3x2 * 3) = 0
(60 + -57x + 9x2) = 0

Solving
60 + -57x + 9x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(20 + -19x + 3x2) = 0

Factor a trinomial.
3((4 + -3x)(5 + -1x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor '(4 + -3x)' equal to zero and attempt to solve:

Simplifying
4 + -3x = 0

Solving
4 + -3x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3x = 0 + -4
-3x = 0 + -4

Combine like terms: 0 + -4 = -4
-3x = -4

Divide each side by '-3'.
x = 1.333333333

Simplifying
x = 1.333333333
Subproblem 2
Set the factor '(5 + -1x)' equal to zero and attempt to solve:

Simplifying
5 + -1x = 0

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

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

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

Divide each side by '-1'.
x = 5

Simplifying
x = 5
Solution
x = {1.333333333, 5}