(3x-5)(4x+8)=0

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Solution for (3x-5)(4x+8)=0 equation: 


Simplifying
(3x + -5)(4x + 8) = 0

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

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

Multiply (-5 + 3x) * (8 + 4x)
(-5(8 + 4x) + 3x * (8 + 4x)) = 0
((8 * -5 + 4x * -5) + 3x * (8 + 4x)) = 0
((-40 + -20x) + 3x * (8 + 4x)) = 0
(-40 + -20x + (8 * 3x + 4x * 3x)) = 0
(-40 + -20x + (24x + 12x2)) = 0

Combine like terms: -20x + 24x = 4x
(-40 + 4x + 12x2) = 0

Solving
-40 + 4x + 12x2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-10 + x + 3x2) = 0

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

Ignore the factor 4.

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

Simplifying
-2 + -1x = 0

Solving
-2 + -1x = 0

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

Add '2' to each side of the equation.
-2 + 2 + -1x = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -1x = 0 + 2
-1x = 0 + 2

Combine like terms: 0 + 2 = 2
-1x = 2

Divide each side by '-1'.
x = -2

Simplifying
x = -2

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 = {-2, 1.666666667}

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