9(x+1)3(2x-4)=0

Solution for 9(x+1)3(2x-4)=0 equation:

Simplifying
9(x + 1) * 3(2x + -4) = 0

Reorder the terms:
9(1 + x) * 3(2x + -4) = 0

Reorder the terms:
9(1 + x) * 3(-4 + 2x) = 0

Reorder the terms for easier multiplication:
9 * 3(1 + x)(-4 + 2x) = 0

Multiply 9 * 3
27(1 + x)(-4 + 2x) = 0

Multiply (1 + x) * (-4 + 2x)
27(1(-4 + 2x) + x(-4 + 2x)) = 0
27((-4 * 1 + 2x * 1) + x(-4 + 2x)) = 0
27((-4 + 2x) + x(-4 + 2x)) = 0
27(-4 + 2x + (-4 * x + 2x * x)) = 0
27(-4 + 2x + (-4x + 2x2)) = 0

Combine like terms: 2x + -4x = -2x
27(-4 + -2x + 2x2) = 0
(-4 * 27 + -2x * 27 + 2x2 * 27) = 0
(-108 + -54x + 54x2) = 0

Solving
-108 + -54x + 54x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '54'.
54(-2 + -1x + x2) = 0

Factor a trinomial.
54((-1 + -1x)(2 + -1x)) = 0

Ignore the factor 54.
Subproblem 1
Set the factor '(-1 + -1x)' equal to zero and attempt to solve:

Simplifying
-1 + -1x = 0

Solving
-1 + -1x = 0

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

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

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

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

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

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

Simplifying
2 + -1x = 0

Solving
2 + -1x = 0

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

Add '-2' to each side of the equation.
2 + -2 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-1, 2}