(3x+18)(9x-27)=0

Solution for (3x+18)(9x-27)=0 equation:

Simplifying
(3x + 18)(9x + -27) = 0

Reorder the terms:
(18 + 3x)(9x + -27) = 0

Reorder the terms:
(18 + 3x)(-27 + 9x) = 0

Multiply (18 + 3x) * (-27 + 9x)
(18(-27 + 9x) + 3x * (-27 + 9x)) = 0
((-27 * 18 + 9x * 18) + 3x * (-27 + 9x)) = 0
((-486 + 162x) + 3x * (-27 + 9x)) = 0
(-486 + 162x + (-27 * 3x + 9x * 3x)) = 0
(-486 + 162x + (-81x + 27x2)) = 0

Combine like terms: 162x + -81x = 81x
(-486 + 81x + 27x2) = 0

Solving
-486 + 81x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '27'.
27(-18 + 3x + x2) = 0

Factor a trinomial.
27((-6 + -1x)(3 + -1x)) = 0

Ignore the factor 27.
Subproblem 1
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
Subproblem 2
Set the factor '(3 + -1x)' equal to zero and attempt to solve:

Simplifying
3 + -1x = 0

Solving
3 + -1x = 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 + -1x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -1x = 0 + -3
-1x = 0 + -3

Combine like terms: 0 + -3 = -3
-1x = -3

Divide each side by '-1'.
x = 3

Simplifying
x = 3
Solution
x = {-6, 3}