(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 + -1x + 3x2) = 0

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

Ignore the factor 4.

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 '(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
Solution
x = {-1.666666667, 2}

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