(3a-5b)(3a-5b)=0

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Solution for (3a-5b)(3a-5b)=0 equation: 


Simplifying
(3a + -5b)(3a + -5b) = 0

Multiply (3a + -5b) * (3a + -5b)
(3a * (3a + -5b) + -5b * (3a + -5b)) = 0
((3a * 3a + -5b * 3a) + -5b * (3a + -5b)) = 0

Reorder the terms:
((-15ab + 9a2) + -5b * (3a + -5b)) = 0
((-15ab + 9a2) + -5b * (3a + -5b)) = 0
(-15ab + 9a2 + (3a * -5b + -5b * -5b)) = 0
(-15ab + 9a2 + (-15ab + 25b2)) = 0

Reorder the terms:
(-15ab + -15ab + 9a2 + 25b2) = 0

Combine like terms: -15ab + -15ab = -30ab
(-30ab + 9a2 + 25b2) = 0

Solving
-30ab + 9a2 + 25b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -5b)(3a + -5b) = 0


Subproblem 1
Set the factor '(3a + -5b)' equal to zero and attempt to solve:

Simplifying
3a + -5b = 0

Solving
3a + -5b = 0

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

Add '5b' to each side of the equation.
3a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
3a + 0 = 0 + 5b
3a = 0 + 5b
Remove the zero:
3a = 5b

Divide each side by '3'.
a = 1.666666667b

Simplifying
a = 1.666666667b

Subproblem 2
Set the factor '(3a + -5b)' equal to zero and attempt to solve:

Simplifying
3a + -5b = 0

Solving
3a + -5b = 0

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

Add '5b' to each side of the equation.
3a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
3a + 0 = 0 + 5b
3a = 0 + 5b
Remove the zero:
3a = 5b

Divide each side by '3'.
a = 1.666666667b

Simplifying
a = 1.666666667b
Solution
a = {1.666666667b, 1.666666667b}

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