24N-3N^2=48N-9N^2

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Solution for 24N-3N^2=48N-9N^2 equation: 


Simplifying
24N + -3N2 = 48N + -9N2

Solving
24N + -3N2 = 48N + -9N2

Solving for variable 'N'.

Reorder the terms:
24N + -48N + -3N2 + 9N2 = 48N + -9N2 + -48N + 9N2

Combine like terms: 24N + -48N = -24N
-24N + -3N2 + 9N2 = 48N + -9N2 + -48N + 9N2

Combine like terms: -3N2 + 9N2 = 6N2
-24N + 6N2 = 48N + -9N2 + -48N + 9N2

Reorder the terms:
-24N + 6N2 = 48N + -48N + -9N2 + 9N2

Combine like terms: 48N + -48N = 0
-24N + 6N2 = 0 + -9N2 + 9N2
-24N + 6N2 = -9N2 + 9N2

Combine like terms: -9N2 + 9N2 = 0
-24N + 6N2 = 0

Factor out the Greatest Common Factor (GCF), '6N'.
6N(-4 + N) = 0

Ignore the factor 6.

Subproblem 1
Set the factor 'N' equal to zero and attempt to solve:

Simplifying
N = 0

Solving
N = 0

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

Simplifying
N = 0

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

Simplifying
-4 + N = 0

Solving
-4 + N = 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 + N = 0 + 4

Combine like terms: -4 + 4 = 0
0 + N = 0 + 4
N = 0 + 4

Combine like terms: 0 + 4 = 4
N = 4

Simplifying
N = 4
Solution
N = {0, 4}

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