27x^2(x+3)-12(x^2+3x)=0

Solution for 27x^2(x+3)-12(x^2+3x)=0 equation:

Simplifying
27x2(x + 3) + -12(x2 + 3x) = 0

Reorder the terms:
27x2(3 + x) + -12(x2 + 3x) = 0
(3 * 27x2 + x * 27x2) + -12(x2 + 3x) = 0
(81x2 + 27x3) + -12(x2 + 3x) = 0

Reorder the terms:
81x2 + 27x3 + -12(3x + x2) = 0
81x2 + 27x3 + (3x * -12 + x2 * -12) = 0
81x2 + 27x3 + (-36x + -12x2) = 0

Reorder the terms:
-36x + 81x2 + -12x2 + 27x3 = 0

Combine like terms: 81x2 + -12x2 = 69x2
-36x + 69x2 + 27x3 = 0

Solving
-36x + 69x2 + 27x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-12 + 23x + 9x2) = 0

Factor a trinomial.
3x((-3 + -1x)(4 + -9x)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0
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
Subproblem 3
Set the factor '(4 + -9x)' equal to zero and attempt to solve:

Simplifying
4 + -9x = 0

Solving
4 + -9x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -9x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -9x = 0 + -4
-9x = 0 + -4

Combine like terms: 0 + -4 = -4
-9x = -4

Divide each side by '-9'.
x = 0.4444444444

Simplifying
x = 0.4444444444
Solution
x = {0, -3, 0.4444444444}