(3a-5b)(7a-4b)=

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Solution for (3a-5b)(7a-4b)= equation: 


Simplifying
(3a + -5b)(7a + -4b) = 0

Multiply (3a + -5b) * (7a + -4b)
(3a * (7a + -4b) + -5b * (7a + -4b)) = 0
((7a * 3a + -4b * 3a) + -5b * (7a + -4b)) = 0

Reorder the terms:
((-12ab + 21a2) + -5b * (7a + -4b)) = 0
((-12ab + 21a2) + -5b * (7a + -4b)) = 0
(-12ab + 21a2 + (7a * -5b + -4b * -5b)) = 0
(-12ab + 21a2 + (-35ab + 20b2)) = 0

Reorder the terms:
(-12ab + -35ab + 21a2 + 20b2) = 0

Combine like terms: -12ab + -35ab = -47ab
(-47ab + 21a2 + 20b2) = 0

Solving
-47ab + 21a2 + 20b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -5b)(7a + -4b) = 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 '(7a + -4b)' equal to zero and attempt to solve:

Simplifying
7a + -4b = 0

Solving
7a + -4b = 0

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

Add '4b' to each side of the equation.
7a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
7a + 0 = 0 + 4b
7a = 0 + 4b
Remove the zero:
7a = 4b

Divide each side by '7'.
a = 0.5714285714b

Simplifying
a = 0.5714285714b
Solution
a = {1.666666667b, 0.5714285714b}

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