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

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


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

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

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

Multiply (-4 + 3n) * (4 + n)
4(-4(4 + n) + 3n * (4 + n)) = 0
4((4 * -4 + n * -4) + 3n * (4 + n)) = 0
4((-16 + -4n) + 3n * (4 + n)) = 0
4(-16 + -4n + (4 * 3n + n * 3n)) = 0
4(-16 + -4n + (12n + 3n2)) = 0

Combine like terms: -4n + 12n = 8n
4(-16 + 8n + 3n2) = 0
(-16 * 4 + 8n * 4 + 3n2 * 4) = 0
(-64 + 32n + 12n2) = 0

Solving
-64 + 32n + 12n2 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), '4'.
4(-16 + 8n + 3n2) = 0

Factor a trinomial.
4((-4 + -1n)(4 + -3n)) = 0

Ignore the factor 4.

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 '(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 = {-4, 1.333333333}

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