n^2(4n-3)-6n^2(4n-9)=

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Solution for n^2(4n-3)-6n^2(4n-9)= equation:


Simplifying
n2(4n + -3) + -6n2(4n + -9) = 0

Reorder the terms:
n2(-3 + 4n) + -6n2(4n + -9) = 0
(-3 * n2 + 4n * n2) + -6n2(4n + -9) = 0
(-3n2 + 4n3) + -6n2(4n + -9) = 0

Reorder the terms:
-3n2 + 4n3 + -6n2(-9 + 4n) = 0
-3n2 + 4n3 + (-9 * -6n2 + 4n * -6n2) = 0
-3n2 + 4n3 + (54n2 + -24n3) = 0

Reorder the terms:
-3n2 + 54n2 + 4n3 + -24n3 = 0

Combine like terms: -3n2 + 54n2 = 51n2
51n2 + 4n3 + -24n3 = 0

Combine like terms: 4n3 + -24n3 = -20n3
51n2 + -20n3 = 0

Solving
51n2 + -20n3 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(51 + -20n) = 0


Subproblem 1
Set the factor 'n2' equal to zero and attempt to solve:

Simplifying
n2 = 0

Solving
n2 = 0

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

Simplifying
n2 = 0

Take the square root of each side:
n = {0}

Subproblem 2
Set the factor '(51 + -20n)' equal to zero and attempt to solve:

Simplifying
51 + -20n = 0

Solving
51 + -20n = 0

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

Add '-51' to each side of the equation.
51 + -51 + -20n = 0 + -51

Combine like terms: 51 + -51 = 0
0 + -20n = 0 + -51
-20n = 0 + -51

Combine like terms: 0 + -51 = -51
-20n = -51

Divide each side by '-20'.
n = 2.55

Simplifying
n = 2.55
Solution
n = {0, 2.55}

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