8(9x-6)(3x+9)=0

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Solution for 8(9x-6)(3x+9)=0 equation: 


Simplifying
8(9x + -6)(3x + 9) = 0

Reorder the terms:
8(-6 + 9x)(3x + 9) = 0

Reorder the terms:
8(-6 + 9x)(9 + 3x) = 0

Multiply (-6 + 9x) * (9 + 3x)
8(-6(9 + 3x) + 9x * (9 + 3x)) = 0
8((9 * -6 + 3x * -6) + 9x * (9 + 3x)) = 0
8((-54 + -18x) + 9x * (9 + 3x)) = 0
8(-54 + -18x + (9 * 9x + 3x * 9x)) = 0
8(-54 + -18x + (81x + 27x2)) = 0

Combine like terms: -18x + 81x = 63x
8(-54 + 63x + 27x2) = 0
(-54 * 8 + 63x * 8 + 27x2 * 8) = 0
(-432 + 504x + 216x2) = 0

Solving
-432 + 504x + 216x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '72'.
72(-6 + 7x + 3x2) = 0

Factor a trinomial.
72((-3 + -1x)(2 + -3x)) = 0

Ignore the factor 72.

Subproblem 1
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 2
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 = {-3, 0.6666666667}

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