(3n-4)(5n+2)=0

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Solution for (3n-4)(5n+2)=0 equation: 


Simplifying
(3n + -4)(5n + 2) = 0

Reorder the terms:
(-4 + 3n)(5n + 2) = 0

Reorder the terms:
(-4 + 3n)(2 + 5n) = 0

Multiply (-4 + 3n) * (2 + 5n)
(-4(2 + 5n) + 3n * (2 + 5n)) = 0
((2 * -4 + 5n * -4) + 3n * (2 + 5n)) = 0
((-8 + -20n) + 3n * (2 + 5n)) = 0
(-8 + -20n + (2 * 3n + 5n * 3n)) = 0
(-8 + -20n + (6n + 15n2)) = 0

Combine like terms: -20n + 6n = -14n
(-8 + -14n + 15n2) = 0

Solving
-8 + -14n + 15n2 = 0

Solving for variable 'n'.

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


Subproblem 1
Set the factor '(-2 + -5n)' equal to zero and attempt to solve:

Simplifying
-2 + -5n = 0

Solving
-2 + -5n = 0

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

Add '2' to each side of the equation.
-2 + 2 + -5n = 0 + 2

Combine like terms: -2 + 2 = 0
0 + -5n = 0 + 2
-5n = 0 + 2

Combine like terms: 0 + 2 = 2
-5n = 2

Divide each side by '-5'.
n = -0.4

Simplifying
n = -0.4

Subproblem 2
Set the factor '(4 + -3n)' equal to zero and attempt to solve:

Simplifying
4 + -3n = 0

Solving
4 + -3n = 0

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

Add '-4' to each side of the equation.
4 + -4 + -3n = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -3n = 0 + -4
-3n = 0 + -4

Combine like terms: 0 + -4 = -4
-3n = -4

Divide each side by '-3'.
n = 1.333333333

Simplifying
n = 1.333333333
Solution
n = {-0.4, 1.333333333}

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