(3x+6)x(x-3)=9x(9+3x+2)

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Solution for (3x+6)x(x-3)=9x(9+3x+2) equation: 


Simplifying
(3x + 6) * x(x + -3) = 9x(9 + 3x + 2)

Reorder the terms:
(6 + 3x) * x(x + -3) = 9x(9 + 3x + 2)

Reorder the terms:
(6 + 3x) * x(-3 + x) = 9x(9 + 3x + 2)

Reorder the terms for easier multiplication:
x(6 + 3x)(-3 + x) = 9x(9 + 3x + 2)

Multiply (6 + 3x) * (-3 + x)
x(6(-3 + x) + 3x * (-3 + x)) = 9x(9 + 3x + 2)
x((-3 * 6 + x * 6) + 3x * (-3 + x)) = 9x(9 + 3x + 2)
x((-18 + 6x) + 3x * (-3 + x)) = 9x(9 + 3x + 2)
x(-18 + 6x + (-3 * 3x + x * 3x)) = 9x(9 + 3x + 2)
x(-18 + 6x + (-9x + 3x2)) = 9x(9 + 3x + 2)

Combine like terms: 6x + -9x = -3x
x(-18 + -3x + 3x2) = 9x(9 + 3x + 2)
(-18 * x + -3x * x + 3x2 * x) = 9x(9 + 3x + 2)
(-18x + -3x2 + 3x3) = 9x(9 + 3x + 2)

Reorder the terms:
-18x + -3x2 + 3x3 = 9x(9 + 2 + 3x)

Combine like terms: 9 + 2 = 11
-18x + -3x2 + 3x3 = 9x(11 + 3x)
-18x + -3x2 + 3x3 = (11 * 9x + 3x * 9x)
-18x + -3x2 + 3x3 = (99x + 27x2)

Solving
-18x + -3x2 + 3x3 = 99x + 27x2

Solving for variable 'x'.

Reorder the terms:
-18x + -99x + -3x2 + -27x2 + 3x3 = 99x + 27x2 + -99x + -27x2

Combine like terms: -18x + -99x = -117x
-117x + -3x2 + -27x2 + 3x3 = 99x + 27x2 + -99x + -27x2

Combine like terms: -3x2 + -27x2 = -30x2
-117x + -30x2 + 3x3 = 99x + 27x2 + -99x + -27x2

Reorder the terms:
-117x + -30x2 + 3x3 = 99x + -99x + 27x2 + -27x2

Combine like terms: 99x + -99x = 0
-117x + -30x2 + 3x3 = 0 + 27x2 + -27x2
-117x + -30x2 + 3x3 = 27x2 + -27x2

Combine like terms: 27x2 + -27x2 = 0
-117x + -30x2 + 3x3 = 0

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-39 + -10x + x2) = 0

Factor a trinomial.
3x((-3 + -1x)(13 + -1x)) = 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 '(13 + -1x)' equal to zero and attempt to solve:

Simplifying
13 + -1x = 0

Solving
13 + -1x = 0

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

Add '-13' to each side of the equation.
13 + -13 + -1x = 0 + -13

Combine like terms: 13 + -13 = 0
0 + -1x = 0 + -13
-1x = 0 + -13

Combine like terms: 0 + -13 = -13
-1x = -13

Divide each side by '-1'.
x = 13

Simplifying
x = 13
Solution
x = {0, -3, 13}

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