(3x+5)(8-2x)=0

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Solution for (3x+5)(8-2x)=0 equation: 


Simplifying
(3x + 5)(8 + -2x) = 0

Reorder the terms:
(5 + 3x)(8 + -2x) = 0

Multiply (5 + 3x) * (8 + -2x)
(5(8 + -2x) + 3x * (8 + -2x)) = 0
((8 * 5 + -2x * 5) + 3x * (8 + -2x)) = 0
((40 + -10x) + 3x * (8 + -2x)) = 0
(40 + -10x + (8 * 3x + -2x * 3x)) = 0
(40 + -10x + (24x + -6x2)) = 0

Combine like terms: -10x + 24x = 14x
(40 + 14x + -6x2) = 0

Solving
40 + 14x + -6x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(20 + 7x + -3x2) = 0

Factor a trinomial.
2((4 + -1x)(5 + 3x)) = 0

Ignore the factor 2.

Subproblem 1
Set the factor '(4 + -1x)' equal to zero and attempt to solve:

Simplifying
4 + -1x = 0

Solving
4 + -1x = 0

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

Add '-4' to each side of the equation.
4 + -4 + -1x = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -1x = 0 + -4
-1x = 0 + -4

Combine like terms: 0 + -4 = -4
-1x = -4

Divide each side by '-1'.
x = 4

Simplifying
x = 4

Subproblem 2
Set the factor '(5 + 3x)' equal to zero and attempt to solve:

Simplifying
5 + 3x = 0

Solving
5 + 3x = 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 + 3x = 0 + -5

Combine like terms: 5 + -5 = 0
0 + 3x = 0 + -5
3x = 0 + -5

Combine like terms: 0 + -5 = -5
3x = -5

Divide each side by '3'.
x = -1.666666667

Simplifying
x = -1.666666667
Solution
x = {4, -1.666666667}

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