6(x-54)(x+9)=0

Solution for 6(x-54)(x+9)=0 equation:

Simplifying
6(x + -54)(x + 9) = 0

Reorder the terms:
6(-54 + x)(x + 9) = 0

Reorder the terms:
6(-54 + x)(9 + x) = 0

Multiply (-54 + x) * (9 + x)
6(-54(9 + x) + x(9 + x)) = 0
6((9 * -54 + x * -54) + x(9 + x)) = 0
6((-486 + -54x) + x(9 + x)) = 0
6(-486 + -54x + (9 * x + x * x)) = 0
6(-486 + -54x + (9x + x2)) = 0

Combine like terms: -54x + 9x = -45x
6(-486 + -45x + x2) = 0
(-486 * 6 + -45x * 6 + x2 * 6) = 0
(-2916 + -270x + 6x2) = 0

Solving
-2916 + -270x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-486 + -45x + x2) = 0

Factor a trinomial.
6((-9 + -1x)(54 + -1x)) = 0

Ignore the factor 6.
Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9
Subproblem 2
Set the factor '(54 + -1x)' equal to zero and attempt to solve:

Simplifying
54 + -1x = 0

Solving
54 + -1x = 0

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

Add '-54' to each side of the equation.
54 + -54 + -1x = 0 + -54

Combine like terms: 54 + -54 = 0
0 + -1x = 0 + -54
-1x = 0 + -54

Combine like terms: 0 + -54 = -54
-1x = -54

Divide each side by '-1'.
x = 54

Simplifying
x = 54
Solution
x = {-9, 54}