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

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


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

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

Multiply (8 + 3x) * (3 + -2x)
(8(3 + -2x) + 3x * (3 + -2x)) = 0
((3 * 8 + -2x * 8) + 3x * (3 + -2x)) = 0
((24 + -16x) + 3x * (3 + -2x)) = 0
(24 + -16x + (3 * 3x + -2x * 3x)) = 0
(24 + -16x + (9x + -6x2)) = 0

Combine like terms: -16x + 9x = -7x
(24 + -7x + -6x2) = 0

Solving
24 + -7x + -6x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(3 + -2x)' equal to zero and attempt to solve:

Simplifying
3 + -2x = 0

Solving
3 + -2x = 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 + -2x = 0 + -3

Combine like terms: 3 + -3 = 0
0 + -2x = 0 + -3
-2x = 0 + -3

Combine like terms: 0 + -3 = -3
-2x = -3

Divide each side by '-2'.
x = 1.5

Simplifying
x = 1.5

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 = {1.5, -2.666666667}

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