(4n+8)(5n-2)=

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Solution for (4n+8)(5n-2)= equation: 


Simplifying
(4n + 8)(5n + -2) = 0

Reorder the terms:
(8 + 4n)(5n + -2) = 0

Reorder the terms:
(8 + 4n)(-2 + 5n) = 0

Multiply (8 + 4n) * (-2 + 5n)
(8(-2 + 5n) + 4n * (-2 + 5n)) = 0
((-2 * 8 + 5n * 8) + 4n * (-2 + 5n)) = 0
((-16 + 40n) + 4n * (-2 + 5n)) = 0
(-16 + 40n + (-2 * 4n + 5n * 4n)) = 0
(-16 + 40n + (-8n + 20n2)) = 0

Combine like terms: 40n + -8n = 32n
(-16 + 32n + 20n2) = 0

Solving
-16 + 32n + 20n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-4 + 8n + 5n2) = 0

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

Ignore the factor 4.

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

Simplifying
-2 + -1n = 0

Solving
-2 + -1n = 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 + -1n = 0 + 2

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

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

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

Simplifying
n = -2

Subproblem 2
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
Solution
n = {-2, 0.4}

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