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

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


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

Reorder the terms:
(5 + 3x)(2x + -8) = 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((-5 + -3x)(4 + -1x)) = 0

Ignore the factor 2.

Subproblem 1
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

Subproblem 2
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
Solution
x = {-1.666666667, 4}

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