(3x+24)(9x-54)=

Solution for (3x+24)(9x-54)= equation:

Simplifying
(3x + 24)(9x + -54) = 0

Reorder the terms:
(24 + 3x)(9x + -54) = 0

Reorder the terms:
(24 + 3x)(-54 + 9x) = 0

Multiply (24 + 3x) * (-54 + 9x)
(24(-54 + 9x) + 3x * (-54 + 9x)) = 0
((-54 * 24 + 9x * 24) + 3x * (-54 + 9x)) = 0
((-1296 + 216x) + 3x * (-54 + 9x)) = 0
(-1296 + 216x + (-54 * 3x + 9x * 3x)) = 0
(-1296 + 216x + (-162x + 27x2)) = 0

Combine like terms: 216x + -162x = 54x
(-1296 + 54x + 27x2) = 0

Solving
-1296 + 54x + 27x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '27'.
27(-48 + 2x + x2) = 0

Factor a trinomial.
27((-8 + -1x)(6 + -1x)) = 0

Ignore the factor 27.
Subproblem 1
Set the factor '(-8 + -1x)' equal to zero and attempt to solve:

Simplifying
-8 + -1x = 0

Solving
-8 + -1x = 0

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

Add '8' to each side of the equation.
-8 + 8 + -1x = 0 + 8

Combine like terms: -8 + 8 = 0
0 + -1x = 0 + 8
-1x = 0 + 8

Combine like terms: 0 + 8 = 8
-1x = 8

Divide each side by '-1'.
x = -8

Simplifying
x = -8
Subproblem 2
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 = {-8, 6}