(3a+2b)(5a-4b)=

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Solution for (3a+2b)(5a-4b)= equation: 


Simplifying
(3a + 2b)(5a + -4b) = 0

Multiply (3a + 2b) * (5a + -4b)
(3a * (5a + -4b) + 2b * (5a + -4b)) = 0
((5a * 3a + -4b * 3a) + 2b * (5a + -4b)) = 0

Reorder the terms:
((-12ab + 15a2) + 2b * (5a + -4b)) = 0
((-12ab + 15a2) + 2b * (5a + -4b)) = 0
(-12ab + 15a2 + (5a * 2b + -4b * 2b)) = 0
(-12ab + 15a2 + (10ab + -8b2)) = 0

Reorder the terms:
(-12ab + 10ab + 15a2 + -8b2) = 0

Combine like terms: -12ab + 10ab = -2ab
(-2ab + 15a2 + -8b2) = 0

Solving
-2ab + 15a2 + -8b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -4b)(3a + 2b) = 0


Subproblem 1
Set the factor '(5a + -4b)' equal to zero and attempt to solve:

Simplifying
5a + -4b = 0

Solving
5a + -4b = 0

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

Add '4b' to each side of the equation.
5a + -4b + 4b = 0 + 4b

Combine like terms: -4b + 4b = 0
5a + 0 = 0 + 4b
5a = 0 + 4b
Remove the zero:
5a = 4b

Divide each side by '5'.
a = 0.8b

Simplifying
a = 0.8b

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 = {0.8b, -0.6666666667b}

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