6x(x-3)(2x+9)=0

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Solution for 6x(x-3)(2x+9)=0 equation: 


Simplifying
6x(x + -3)(2x + 9) = 0

Reorder the terms:
6x(-3 + x)(2x + 9) = 0

Reorder the terms:
6x(-3 + x)(9 + 2x) = 0

Multiply (-3 + x) * (9 + 2x)
6x(-3(9 + 2x) + x(9 + 2x)) = 0
6x((9 * -3 + 2x * -3) + x(9 + 2x)) = 0
6x((-27 + -6x) + x(9 + 2x)) = 0
6x(-27 + -6x + (9 * x + 2x * x)) = 0
6x(-27 + -6x + (9x + 2x2)) = 0

Combine like terms: -6x + 9x = 3x
6x(-27 + 3x + 2x2) = 0
(-27 * 6x + 3x * 6x + 2x2 * 6x) = 0
(-162x + 18x2 + 12x3) = 0

Solving
-162x + 18x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-27 + 3x + 2x2) = 0

Factor a trinomial.
6x((-9 + -2x)(3 + -1x)) = 0

Ignore the factor 6.

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 '(-9 + -2x)' equal to zero and attempt to solve:

Simplifying
-9 + -2x = 0

Solving
-9 + -2x = 0

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

Add '9' to each side of the equation.
-9 + 9 + -2x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -2x = 0 + 9
-2x = 0 + 9

Combine like terms: 0 + 9 = 9
-2x = 9

Divide each side by '-2'.
x = -4.5

Simplifying
x = -4.5

Subproblem 3
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
Solution
x = {0, -4.5, 3}

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