(3x+27)*(2x-4)=0

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Solution for (3x+27)*(2x-4)=0 equation: 


Simplifying
(3x + 27)(2x + -4) = 0

Reorder the terms:
(27 + 3x)(2x + -4) = 0

Reorder the terms:
(27 + 3x)(-4 + 2x) = 0

Multiply (27 + 3x) * (-4 + 2x)
(27(-4 + 2x) + 3x * (-4 + 2x)) = 0
((-4 * 27 + 2x * 27) + 3x * (-4 + 2x)) = 0
((-108 + 54x) + 3x * (-4 + 2x)) = 0
(-108 + 54x + (-4 * 3x + 2x * 3x)) = 0
(-108 + 54x + (-12x + 6x2)) = 0

Combine like terms: 54x + -12x = 42x
(-108 + 42x + 6x2) = 0

Solving
-108 + 42x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-18 + 7x + x2) = 0

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

Ignore the factor 6.

Subproblem 1
Set the factor '(-9 + -1x)' equal to zero and attempt to solve:

Simplifying
-9 + -1x = 0

Solving
-9 + -1x = 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 + -1x = 0 + 9

Combine like terms: -9 + 9 = 0
0 + -1x = 0 + 9
-1x = 0 + 9

Combine like terms: 0 + 9 = 9
-1x = 9

Divide each side by '-1'.
x = -9

Simplifying
x = -9

Subproblem 2
Set the factor '(2 + -1x)' equal to zero and attempt to solve:

Simplifying
2 + -1x = 0

Solving
2 + -1x = 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 + -1x = 0 + -2

Combine like terms: 2 + -2 = 0
0 + -1x = 0 + -2
-1x = 0 + -2

Combine like terms: 0 + -2 = -2
-1x = -2

Divide each side by '-1'.
x = 2

Simplifying
x = 2
Solution
x = {-9, 2}

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