(3x+6)(6x-4)=0

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Solution for (3x+6)(6x-4)=0 equation: 


Simplifying
(3x + 6)(6x + -4) = 0

Reorder the terms:
(6 + 3x)(6x + -4) = 0

Reorder the terms:
(6 + 3x)(-4 + 6x) = 0

Multiply (6 + 3x) * (-4 + 6x)
(6(-4 + 6x) + 3x * (-4 + 6x)) = 0
((-4 * 6 + 6x * 6) + 3x * (-4 + 6x)) = 0
((-24 + 36x) + 3x * (-4 + 6x)) = 0
(-24 + 36x + (-4 * 3x + 6x * 3x)) = 0
(-24 + 36x + (-12x + 18x2)) = 0

Combine like terms: 36x + -12x = 24x
(-24 + 24x + 18x2) = 0

Solving
-24 + 24x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '6'.
6(-4 + 4x + 3x2) = 0

Factor a trinomial.
6((-2 + -1x)(2 + -3x)) = 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 '(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 = {-2, 0.6666666667}

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