(3x-8)(5-x)=0

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Solution for (3x-8)(5-x)=0 equation: 


Simplifying
(3x + -8)(5 + -1x) = 0

Reorder the terms:
(-8 + 3x)(5 + -1x) = 0

Multiply (-8 + 3x) * (5 + -1x)
(-8(5 + -1x) + 3x * (5 + -1x)) = 0
((5 * -8 + -1x * -8) + 3x * (5 + -1x)) = 0
((-40 + 8x) + 3x * (5 + -1x)) = 0
(-40 + 8x + (5 * 3x + -1x * 3x)) = 0
(-40 + 8x + (15x + -3x2)) = 0

Combine like terms: 8x + 15x = 23x
(-40 + 23x + -3x2) = 0

Solving
-40 + 23x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-5 + x)(8 + -3x) = 0


Subproblem 1
Set the factor '(-5 + x)' equal to zero and attempt to solve:

Simplifying
-5 + x = 0

Solving
-5 + x = 0

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

Add '5' to each side of the equation.
-5 + 5 + x = 0 + 5

Combine like terms: -5 + 5 = 0
0 + x = 0 + 5
x = 0 + 5

Combine like terms: 0 + 5 = 5
x = 5

Simplifying
x = 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 = {5, 2.666666667}

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