(3x-9)(2x+4)=0

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Solution for (3x-9)(2x+4)=0 equation: 


Simplifying
(3x + -9)(2x + 4) = 0

Reorder the terms:
(-9 + 3x)(2x + 4) = 0

Reorder the terms:
(-9 + 3x)(4 + 2x) = 0

Multiply (-9 + 3x) * (4 + 2x)
(-9(4 + 2x) + 3x * (4 + 2x)) = 0
((4 * -9 + 2x * -9) + 3x * (4 + 2x)) = 0
((-36 + -18x) + 3x * (4 + 2x)) = 0
(-36 + -18x + (4 * 3x + 2x * 3x)) = 0
(-36 + -18x + (12x + 6x2)) = 0

Combine like terms: -18x + 12x = -6x
(-36 + -6x + 6x2) = 0

Solving
-36 + -6x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-6 + -1x + x2) = 0

Factor a trinomial.
6((-2 + -1x)(3 + -1x)) = 0

Ignore the factor 6.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-2, 3}

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