(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 + -1x + 3x2) = 0

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

Ignore the factor 2.

Subproblem 1
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

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 = {-2.666666667, 3}

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