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

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


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

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

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

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

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

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

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3'.
3(-30 + 11x + -1x2) = 0

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

Ignore the factor 3.

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

Simplifying
-6 + x = 0

Solving
-6 + x = 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 + x = 0 + 6

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

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

Simplifying
x = 6

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 = {6, 5}

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