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

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


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

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

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

Multiply (-8 + 3x) * (6 + 2x)
(-8(6 + 2x) + 3x * (6 + 2x)) = 0
((6 * -8 + 2x * -8) + 3x * (6 + 2x)) = 0
((-48 + -16x) + 3x * (6 + 2x)) = 0
(-48 + -16x + (6 * 3x + 2x * 3x)) = 0
(-48 + -16x + (18x + 6x2)) = 0

Combine like terms: -16x + 18x = 2x
(-48 + 2x + 6x2) = 0

Solving
-48 + 2x + 6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-24 + x + 3x2) = 0

Factor a trinomial.
2((-3 + -1x)(8 + -3x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
Set the factor '(8 + -3x)' equal to zero and attempt to solve:

Simplifying
8 + -3x = 0

Solving
8 + -3x = 0

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

Add '-8' to each side of the equation.
8 + -8 + -3x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -3x = 0 + -8
-3x = 0 + -8

Combine like terms: 0 + -8 = -8
-3x = -8

Divide each side by '-3'.
x = 2.666666667

Simplifying
x = 2.666666667
Solution
x = {-3, 2.666666667}

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