n^2=2(n-5)(n-5)+50

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Solution for n^2=2(n-5)(n-5)+50 equation: 


Simplifying
n2 = 2(n + -5)(n + -5) + 50

Reorder the terms:
n2 = 2(-5 + n)(n + -5) + 50

Reorder the terms:
n2 = 2(-5 + n)(-5 + n) + 50

Multiply (-5 + n) * (-5 + n)
n2 = 2(-5(-5 + n) + n(-5 + n)) + 50
n2 = 2((-5 * -5 + n * -5) + n(-5 + n)) + 50
n2 = 2((25 + -5n) + n(-5 + n)) + 50
n2 = 2(25 + -5n + (-5 * n + n * n)) + 50
n2 = 2(25 + -5n + (-5n + n2)) + 50

Combine like terms: -5n + -5n = -10n
n2 = 2(25 + -10n + n2) + 50
n2 = (25 * 2 + -10n * 2 + n2 * 2) + 50
n2 = (50 + -20n + 2n2) + 50

Reorder the terms:
n2 = 50 + 50 + -20n + 2n2

Combine like terms: 50 + 50 = 100
n2 = 100 + -20n + 2n2

Solving
n2 = 100 + -20n + 2n2

Solving for variable 'n'.

Reorder the terms:
-100 + 20n + n2 + -2n2 = 100 + -20n + 2n2 + -100 + 20n + -2n2

Combine like terms: n2 + -2n2 = -1n2
-100 + 20n + -1n2 = 100 + -20n + 2n2 + -100 + 20n + -2n2

Reorder the terms:
-100 + 20n + -1n2 = 100 + -100 + -20n + 20n + 2n2 + -2n2

Combine like terms: 100 + -100 = 0
-100 + 20n + -1n2 = 0 + -20n + 20n + 2n2 + -2n2
-100 + 20n + -1n2 = -20n + 20n + 2n2 + -2n2

Combine like terms: -20n + 20n = 0
-100 + 20n + -1n2 = 0 + 2n2 + -2n2
-100 + 20n + -1n2 = 2n2 + -2n2

Combine like terms: 2n2 + -2n2 = 0
-100 + 20n + -1n2 = 0

Factor a trinomial.
(-10 + n)(10 + -1n) = 0


Subproblem 1
Set the factor '(-10 + n)' equal to zero and attempt to solve:

Simplifying
-10 + n = 0

Solving
-10 + n = 0

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

Add '10' to each side of the equation.
-10 + 10 + n = 0 + 10

Combine like terms: -10 + 10 = 0
0 + n = 0 + 10
n = 0 + 10

Combine like terms: 0 + 10 = 10
n = 10

Simplifying
n = 10

Subproblem 2
Set the factor '(10 + -1n)' equal to zero and attempt to solve:

Simplifying
10 + -1n = 0

Solving
10 + -1n = 0

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

Add '-10' to each side of the equation.
10 + -10 + -1n = 0 + -10

Combine like terms: 10 + -10 = 0
0 + -1n = 0 + -10
-1n = 0 + -10

Combine like terms: 0 + -10 = -10
-1n = -10

Divide each side by '-1'.
n = 10

Simplifying
n = 10
Solution
n = {10, 10}

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