(6x-18)(3x+2)=0

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Solution for (6x-18)(3x+2)=0 equation: 


Simplifying
(6x + -18)(3x + 2) = 0

Reorder the terms:
(-18 + 6x)(3x + 2) = 0

Reorder the terms:
(-18 + 6x)(2 + 3x) = 0

Multiply (-18 + 6x) * (2 + 3x)
(-18(2 + 3x) + 6x * (2 + 3x)) = 0
((2 * -18 + 3x * -18) + 6x * (2 + 3x)) = 0
((-36 + -54x) + 6x * (2 + 3x)) = 0
(-36 + -54x + (2 * 6x + 3x * 6x)) = 0
(-36 + -54x + (12x + 18x2)) = 0

Combine like terms: -54x + 12x = -42x
(-36 + -42x + 18x2) = 0

Solving
-36 + -42x + 18x2 = 0

Solving for variable 'x'.

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

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

Ignore the factor 6.

Subproblem 1
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

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 = {-0.6666666667, 3}

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