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

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


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

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

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

Multiply (-9 + 2x) * (6 + x)
6x(-9(6 + x) + 2x * (6 + x)) = 0
6x((6 * -9 + x * -9) + 2x * (6 + x)) = 0
6x((-54 + -9x) + 2x * (6 + x)) = 0
6x(-54 + -9x + (6 * 2x + x * 2x)) = 0
6x(-54 + -9x + (12x + 2x2)) = 0

Combine like terms: -9x + 12x = 3x
6x(-54 + 3x + 2x2) = 0
(-54 * 6x + 3x * 6x + 2x2 * 6x) = 0
(-324x + 18x2 + 12x3) = 0

Solving
-324x + 18x2 + 12x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6x'.
6x(-54 + 3x + 2x2) = 0

Factor a trinomial.
6x((-6 + -1x)(9 + -2x)) = 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 '(-6 + -1x)' equal to zero and attempt to solve:

Simplifying
-6 + -1x = 0

Solving
-6 + -1x = 0

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

Add '6' to each side of the equation.
-6 + 6 + -1x = 0 + 6

Combine like terms: -6 + 6 = 0
0 + -1x = 0 + 6
-1x = 0 + 6

Combine like terms: 0 + 6 = 6
-1x = 6

Divide each side by '-1'.
x = -6

Simplifying
x = -6

Subproblem 3
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
Solution
x = {0, -6, 4.5}

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