(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 = 23x
(8 + 23x + -3x2) = 0

Solving
8 + 23x + -3x2 = 0

Solving for variable 'x'.

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


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

Simplifying
8 + -1x = 0

Solving
8 + -1x = 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 + -1x = 0 + -8

Combine like terms: 8 + -8 = 0
0 + -1x = 0 + -8
-1x = 0 + -8

Combine like terms: 0 + -8 = -8
-1x = -8

Divide each side by '-1'.
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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