3x(x-6)(x-5)=0

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Solution for 3x(x-6)(x-5)=0 equation: 


Simplifying
3x(x + -6)(x + -5) = 0

Reorder the terms:
3x(-6 + x)(x + -5) = 0

Reorder the terms:
3x(-6 + x)(-5 + x) = 0

Multiply (-6 + x) * (-5 + x)
3x(-6(-5 + x) + x(-5 + x)) = 0
3x((-5 * -6 + x * -6) + x(-5 + x)) = 0
3x((30 + -6x) + x(-5 + x)) = 0
3x(30 + -6x + (-5 * x + x * x)) = 0
3x(30 + -6x + (-5x + x2)) = 0

Combine like terms: -6x + -5x = -11x
3x(30 + -11x + x2) = 0
(30 * 3x + -11x * 3x + x2 * 3x) = 0
(90x + -33x2 + 3x3) = 0

Solving
90x + -33x2 + 3x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(30 + -11x + x2) = 0

Factor a trinomial.
3x((5 + -1x)(6 + -1x)) = 0

Ignore the factor 3.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

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

Subproblem 3
Set the factor '(6 + -1x)' equal to zero and attempt to solve:

Simplifying
6 + -1x = 0

Solving
6 + -1x = 0

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

Add '-6' to each side of the equation.
6 + -6 + -1x = 0 + -6

Combine like terms: 6 + -6 = 0
0 + -1x = 0 + -6
-1x = 0 + -6

Combine like terms: 0 + -6 = -6
-1x = -6

Divide each side by '-1'.
x = 6

Simplifying
x = 6
Solution
x = {0, 5, 6}

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