a^2-18ab+65b^2=0

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Solution for a^2-18ab+65b^2=0 equation: 


Simplifying
a2 + -18ab + 65b2 = 0

Reorder the terms:
-18ab + a2 + 65b2 = 0

Solving
-18ab + a2 + 65b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -13b)(a + -5b) = 0


Subproblem 1
Set the factor '(a + -13b)' equal to zero and attempt to solve:

Simplifying
a + -13b = 0

Solving
a + -13b = 0

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

Add '13b' to each side of the equation.
a + -13b + 13b = 0 + 13b

Combine like terms: -13b + 13b = 0
a + 0 = 0 + 13b
a = 0 + 13b
Remove the zero:
a = 13b

Simplifying
a = 13b

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

Simplifying
a + -5b = 0

Solving
a + -5b = 0

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

Add '5b' to each side of the equation.
a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
a + 0 = 0 + 5b
a = 0 + 5b
Remove the zero:
a = 5b

Simplifying
a = 5b
Solution
a = {13b, 5b}

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