(3a-2b)*(5a-6b)=0

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Solution for (3a-2b)*(5a-6b)=0 equation: 


Simplifying
(3a + -2b)(5a + -6b) = 0

Multiply (3a + -2b) * (5a + -6b)
(3a * (5a + -6b) + -2b * (5a + -6b)) = 0
((5a * 3a + -6b * 3a) + -2b * (5a + -6b)) = 0

Reorder the terms:
((-18ab + 15a2) + -2b * (5a + -6b)) = 0
((-18ab + 15a2) + -2b * (5a + -6b)) = 0
(-18ab + 15a2 + (5a * -2b + -6b * -2b)) = 0
(-18ab + 15a2 + (-10ab + 12b2)) = 0

Reorder the terms:
(-18ab + -10ab + 15a2 + 12b2) = 0

Combine like terms: -18ab + -10ab = -28ab
(-28ab + 15a2 + 12b2) = 0

Solving
-28ab + 15a2 + 12b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -6b)(3a + -2b) = 0


Subproblem 1
Set the factor '(5a + -6b)' equal to zero and attempt to solve:

Simplifying
5a + -6b = 0

Solving
5a + -6b = 0

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

Add '6b' to each side of the equation.
5a + -6b + 6b = 0 + 6b

Combine like terms: -6b + 6b = 0
5a + 0 = 0 + 6b
5a = 0 + 6b
Remove the zero:
5a = 6b

Divide each side by '5'.
a = 1.2b

Simplifying
a = 1.2b

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

Simplifying
3a + -2b = 0

Solving
3a + -2b = 0

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

Add '2b' to each side of the equation.
3a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
3a + 0 = 0 + 2b
3a = 0 + 2b
Remove the zero:
3a = 2b

Divide each side by '3'.
a = 0.6666666667b

Simplifying
a = 0.6666666667b
Solution
a = {1.2b, 0.6666666667b}

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