a(n+2)=7a(n+1)-10an

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Solution for a(n+2)=7a(n+1)-10an equation: 


Simplifying
a(n + 2) = 7a(n + 1) + -10an

Reorder the terms:
a(2 + n) = 7a(n + 1) + -10an
(2 * a + n * a) = 7a(n + 1) + -10an
(2a + an) = 7a(n + 1) + -10an

Reorder the terms:
2a + an = 7a(1 + n) + -10an
2a + an = (1 * 7a + n * 7a) + -10an
2a + an = (7a + 7an) + -10an

Combine like terms: 7an + -10an = -3an
2a + an = 7a + -3an

Solving
2a + an = 7a + -3an

Solving for variable 'a'.

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

Add '-7a' to each side of the equation.
2a + -7a + an = 7a + -7a + -3an

Combine like terms: 2a + -7a = -5a
-5a + an = 7a + -7a + -3an

Combine like terms: 7a + -7a = 0
-5a + an = 0 + -3an
-5a + an = -3an

Add '3an' to each side of the equation.
-5a + an + 3an = -3an + 3an

Combine like terms: an + 3an = 4an
-5a + 4an = -3an + 3an

Combine like terms: -3an + 3an = 0
-5a + 4an = 0

Factor out the Greatest Common Factor (GCF), 'a'.
a(-5 + 4n) = 0


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

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0

Subproblem 2
Set the factor '(-5 + 4n)' equal to zero and attempt to solve:

Simplifying
-5 + 4n = 0

Solving
-5 + 4n = 0

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

Add '5' to each side of the equation.
-5 + 5 + 4n = 0 + 5

Combine like terms: -5 + 5 = 0
0 + 4n = 0 + 5
4n = 0 + 5

Combine like terms: 0 + 5 = 5
4n = 5

Add '-4n' to each side of the equation.
4n + -4n = 5 + -4n

Combine like terms: 4n + -4n = 0
0 = 5 + -4n

Simplifying
0 = 5 + -4n

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
a = {0}

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