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

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


Simplifying
(3x + -8)(2 + -1x) = 0

Reorder the terms:
(-8 + 3x)(2 + -1x) = 0

Multiply (-8 + 3x) * (2 + -1x)
(-8(2 + -1x) + 3x * (2 + -1x)) = 0
((2 * -8 + -1x * -8) + 3x * (2 + -1x)) = 0
((-16 + 8x) + 3x * (2 + -1x)) = 0
(-16 + 8x + (2 * 3x + -1x * 3x)) = 0
(-16 + 8x + (6x + -3x2)) = 0

Combine like terms: 8x + 6x = 14x
(-16 + 14x + -3x2) = 0

Solving
-16 + 14x + -3x2 = 0

Solving for variable 'x'.

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


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 '(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
Solution
x = {2.666666667, 2}

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