(3x-1)(8-x)=0

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Solution for (3x-1)(8-x)=0 equation: 


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

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

Multiply (-1 + 3x) * (8 + -1x)
(-1(8 + -1x) + 3x * (8 + -1x)) = 0
((8 * -1 + -1x * -1) + 3x * (8 + -1x)) = 0
((-8 + 1x) + 3x * (8 + -1x)) = 0
(-8 + 1x + (8 * 3x + -1x * 3x)) = 0
(-8 + 1x + (24x + -3x2)) = 0

Combine like terms: 1x + 24x = 25x
(-8 + 25x + -3x2) = 0

Solving
-8 + 25x + -3x2 = 0

Solving for variable 'x'.

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


Subproblem 1
Set the factor '(-8 + x)' equal to zero and attempt to solve:

Simplifying
-8 + x = 0

Solving
-8 + x = 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 + x = 0 + 8

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

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

Simplifying
x = 8

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

Simplifying
1 + -3x = 0

Solving
1 + -3x = 0

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

Add '-1' to each side of the equation.
1 + -1 + -3x = 0 + -1

Combine like terms: 1 + -1 = 0
0 + -3x = 0 + -1
-3x = 0 + -1

Combine like terms: 0 + -1 = -1
-3x = -1

Divide each side by '-3'.
x = 0.3333333333

Simplifying
x = 0.3333333333
Solution
x = {8, 0.3333333333}

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