8(9x+27)(6x-9)=0

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Solution for 8(9x+27)(6x-9)=0 equation: 


Simplifying
8(9x + 27)(6x + -9) = 0

Reorder the terms:
8(27 + 9x)(6x + -9) = 0

Reorder the terms:
8(27 + 9x)(-9 + 6x) = 0

Multiply (27 + 9x) * (-9 + 6x)
8(27(-9 + 6x) + 9x * (-9 + 6x)) = 0
8((-9 * 27 + 6x * 27) + 9x * (-9 + 6x)) = 0
8((-243 + 162x) + 9x * (-9 + 6x)) = 0
8(-243 + 162x + (-9 * 9x + 6x * 9x)) = 0
8(-243 + 162x + (-81x + 54x2)) = 0

Combine like terms: 162x + -81x = 81x
8(-243 + 81x + 54x2) = 0
(-243 * 8 + 81x * 8 + 54x2 * 8) = 0
(-1944 + 648x + 432x2) = 0

Solving
-1944 + 648x + 432x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '216'.
216(-9 + 3x + 2x2) = 0

Factor a trinomial.
216((-3 + -1x)(3 + -2x)) = 0

Ignore the factor 216.

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 '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

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

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

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

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5
Solution
x = {-3, 1.5}

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