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

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


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

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

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

Multiply (-5 + 2n) * (-5 + 2n)
n2(-5(-5 + 2n) + 2n * (-5 + 2n)) = 0
n2((-5 * -5 + 2n * -5) + 2n * (-5 + 2n)) = 0
n2((25 + -10n) + 2n * (-5 + 2n)) = 0
n2(25 + -10n + (-5 * 2n + 2n * 2n)) = 0
n2(25 + -10n + (-10n + 4n2)) = 0

Combine like terms: -10n + -10n = -20n
n2(25 + -20n + 4n2) = 0
(25 * n2 + -20n * n2 + 4n2 * n2) = 0
(25n2 + -20n3 + 4n4) = 0

Solving
25n2 + -20n3 + 4n4 = 0

Solving for variable 'n'.

Factor out the Greatest Common Factor (GCF), 'n2'.
n2(25 + -20n + 4n2) = 0

Factor a trinomial.
n2((5 + -2n)(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 '(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

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, 2.5, 2.5}

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