(12x+3)(18-9x)x=0

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Solution for (12x+3)(18-9x)x=0 equation: 


Simplifying
(12x + 3)(18 + -9x) * x = 0

Reorder the terms:
(3 + 12x)(18 + -9x) * x = 0

Reorder the terms for easier multiplication:
x(3 + 12x)(18 + -9x) = 0

Multiply (3 + 12x) * (18 + -9x)
x(3(18 + -9x) + 12x * (18 + -9x)) = 0
x((18 * 3 + -9x * 3) + 12x * (18 + -9x)) = 0
x((54 + -27x) + 12x * (18 + -9x)) = 0
x(54 + -27x + (18 * 12x + -9x * 12x)) = 0
x(54 + -27x + (216x + -108x2)) = 0

Combine like terms: -27x + 216x = 189x
x(54 + 189x + -108x2) = 0
(54 * x + 189x * x + -108x2 * x) = 0
(54x + 189x2 + -108x3) = 0

Solving
54x + 189x2 + -108x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '27x'.
27x(2 + 7x + -4x2) = 0

Factor a trinomial.
27x((2 + -1x)(1 + 4x)) = 0

Ignore the factor 27.

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 '(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

Subproblem 3
Set the factor '(1 + 4x)' equal to zero and attempt to solve:

Simplifying
1 + 4x = 0

Solving
1 + 4x = 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 + 4x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + 4x = 0 + -1
4x = 0 + -1

Combine like terms: 0 + -1 = -1
4x = -1

Divide each side by '4'.
x = -0.25

Simplifying
x = -0.25
Solution
x = {0, 2, -0.25}

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