(n+4)(4n-10)=0

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Solution for (n+4)(4n-10)=0 equation: 


Simplifying
(n + 4)(4n + -10) = 0

Reorder the terms:
(4 + n)(4n + -10) = 0

Reorder the terms:
(4 + n)(-10 + 4n) = 0

Multiply (4 + n) * (-10 + 4n)
(4(-10 + 4n) + n(-10 + 4n)) = 0
((-10 * 4 + 4n * 4) + n(-10 + 4n)) = 0
((-40 + 16n) + n(-10 + 4n)) = 0
(-40 + 16n + (-10 * n + 4n * n)) = 0
(-40 + 16n + (-10n + 4n2)) = 0

Combine like terms: 16n + -10n = 6n
(-40 + 6n + 4n2) = 0

Solving
-40 + 6n + 4n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-20 + 3n + 2n2) = 0

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

Ignore the factor 2.

Subproblem 1
Set the factor '(-4 + -1n)' equal to zero and attempt to solve:

Simplifying
-4 + -1n = 0

Solving
-4 + -1n = 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 + -1n = 0 + 4

Combine like terms: -4 + 4 = 0
0 + -1n = 0 + 4
-1n = 0 + 4

Combine like terms: 0 + 4 = 4
-1n = 4

Divide each side by '-1'.
n = -4

Simplifying
n = -4

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

Simplifying
5 + -2n = 0

Solving
5 + -2n = 0

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

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

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

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

Divide each side by '-2'.
n = 2.5

Simplifying
n = 2.5
Solution
n = {-4, 2.5}

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