n^2(n-2)(2n-5)=0

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Solution for n^2(n-2)(2n-5)=0 equation: 


Simplifying
n2(n + -2)(2n + -5) = 0

Reorder the terms:
n2(-2 + n)(2n + -5) = 0

Reorder the terms:
n2(-2 + n)(-5 + 2n) = 0

Multiply (-2 + n) * (-5 + 2n)
n2(-2(-5 + 2n) + n(-5 + 2n)) = 0
n2((-5 * -2 + 2n * -2) + n(-5 + 2n)) = 0
n2((10 + -4n) + n(-5 + 2n)) = 0
n2(10 + -4n + (-5 * n + 2n * n)) = 0
n2(10 + -4n + (-5n + 2n2)) = 0

Combine like terms: -4n + -5n = -9n
n2(10 + -9n + 2n2) = 0
(10 * n2 + -9n * n2 + 2n2 * n2) = 0
(10n2 + -9n3 + 2n4) = 0

Solving
10n2 + -9n3 + 2n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(10 + -9n + 2n2) = 0

Factor a trinomial.
n2((2 + -1n)(5 + -2n)) = 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 '(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 3
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 = {0, 2, 2.5}

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