(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 = 7x
(40 + 7x + -3x2) = 0

Solving
40 + 7x + -3x2 = 0

Solving for variable 'x'.

Factor a trinomial.
(5 + -1x)(8 + 3x) = 0


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

Simplifying
5 + -1x = 0

Solving
5 + -1x = 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 + -1x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + -1x = 0 + -5
-1x = 0 + -5

Combine like terms: 0 + -5 = -5
-1x = -5

Divide each side by '-1'.
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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