(3a-4b)(5b-3a)=

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Solution for (3a-4b)(5b-3a)= equation: 


Simplifying
(3a + -4b)(5b + -3a) = 0

Reorder the terms:
(3a + -4b)(-3a + 5b) = 0

Multiply (3a + -4b) * (-3a + 5b)
(3a * (-3a + 5b) + -4b * (-3a + 5b)) = 0
((-3a * 3a + 5b * 3a) + -4b * (-3a + 5b)) = 0

Reorder the terms:
((15ab + -9a2) + -4b * (-3a + 5b)) = 0
((15ab + -9a2) + -4b * (-3a + 5b)) = 0
(15ab + -9a2 + (-3a * -4b + 5b * -4b)) = 0
(15ab + -9a2 + (12ab + -20b2)) = 0

Reorder the terms:
(15ab + 12ab + -9a2 + -20b2) = 0

Combine like terms: 15ab + 12ab = 27ab
(27ab + -9a2 + -20b2) = 0

Solving
27ab + -9a2 + -20b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(-3a + 4b)(3a + -5b) = 0


Subproblem 1
Set the factor '(-3a + 4b)' equal to zero and attempt to solve:

Simplifying
-3a + 4b = 0

Solving
-3a + 4b = 0

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

Add '-4b' to each side of the equation.
-3a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
-3a + 0 = 0 + -4b
-3a = 0 + -4b
Remove the zero:
-3a = -4b

Divide each side by '-3'.
a = 1.333333333b

Simplifying
a = 1.333333333b

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 = {1.333333333b, 1.666666667b}

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