(3x-2)(6x+8)=0

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Solution for (3x-2)(6x+8)=0 equation: 


Simplifying
(3x + -2)(6x + 8) = 0

Reorder the terms:
(-2 + 3x)(6x + 8) = 0

Reorder the terms:
(-2 + 3x)(8 + 6x) = 0

Multiply (-2 + 3x) * (8 + 6x)
(-2(8 + 6x) + 3x * (8 + 6x)) = 0
((8 * -2 + 6x * -2) + 3x * (8 + 6x)) = 0
((-16 + -12x) + 3x * (8 + 6x)) = 0
(-16 + -12x + (8 * 3x + 6x * 3x)) = 0
(-16 + -12x + (24x + 18x2)) = 0

Combine like terms: -12x + 24x = 12x
(-16 + 12x + 18x2) = 0

Solving
-16 + 12x + 18x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-8 + 6x + 9x2) = 0

Factor a trinomial.
2((-4 + -3x)(2 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -3x)' equal to zero and attempt to solve:

Simplifying
-4 + -3x = 0

Solving
-4 + -3x = 0

Move all terms containing x to the left, all other terms to the right.

Add '4' to each side of the equation.
-4 + 4 + -3x = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -3x = 0 + 4
-3x = 0 + 4

Combine like terms: 0 + 4 = 4
-3x = 4

Divide each side by '-3'.
x = -1.333333333

Simplifying
x = -1.333333333

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 = {-1.333333333, 0.6666666667}

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