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

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


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

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

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

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

Multiply (-6 + 9x) * (9 + 2x)
x(-6(9 + 2x) + 9x * (9 + 2x)) = 0
x((9 * -6 + 2x * -6) + 9x * (9 + 2x)) = 0
x((-54 + -12x) + 9x * (9 + 2x)) = 0
x(-54 + -12x + (9 * 9x + 2x * 9x)) = 0
x(-54 + -12x + (81x + 18x2)) = 0

Combine like terms: -12x + 81x = 69x
x(-54 + 69x + 18x2) = 0
(-54 * x + 69x * x + 18x2 * x) = 0
(-54x + 69x2 + 18x3) = 0

Solving
-54x + 69x2 + 18x3 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '3x'.
3x(-18 + 23x + 6x2) = 0

Factor a trinomial.
3x((-9 + -2x)(2 + -3x)) = 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 '(-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 '(2 + -3x)' equal to zero and attempt to solve:

Simplifying
2 + -3x = 0

Solving
2 + -3x = 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 + -3x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -3x = 0 + -2
-3x = 0 + -2

Combine like terms: 0 + -2 = -2
-3x = -2

Divide each side by '-3'.
x = 0.6666666667

Simplifying
x = 0.6666666667
Solution
x = {0, -4.5, 0.6666666667}

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