(5a+4b)(3a-8b)=

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Solution for (5a+4b)(3a-8b)= equation: 


Simplifying
(5a + 4b)(3a + -8b) = 0

Multiply (5a + 4b) * (3a + -8b)
(5a * (3a + -8b) + 4b * (3a + -8b)) = 0
((3a * 5a + -8b * 5a) + 4b * (3a + -8b)) = 0

Reorder the terms:
((-40ab + 15a2) + 4b * (3a + -8b)) = 0
((-40ab + 15a2) + 4b * (3a + -8b)) = 0
(-40ab + 15a2 + (3a * 4b + -8b * 4b)) = 0
(-40ab + 15a2 + (12ab + -32b2)) = 0

Reorder the terms:
(-40ab + 12ab + 15a2 + -32b2) = 0

Combine like terms: -40ab + 12ab = -28ab
(-28ab + 15a2 + -32b2) = 0

Solving
-28ab + 15a2 + -32b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -8b)(5a + 4b) = 0


Subproblem 1
Set the factor '(3a + -8b)' equal to zero and attempt to solve:

Simplifying
3a + -8b = 0

Solving
3a + -8b = 0

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

Add '8b' to each side of the equation.
3a + -8b + 8b = 0 + 8b

Combine like terms: -8b + 8b = 0
3a + 0 = 0 + 8b
3a = 0 + 8b
Remove the zero:
3a = 8b

Divide each side by '3'.
a = 2.666666667b

Simplifying
a = 2.666666667b

Subproblem 2
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
Solution
a = {2.666666667b, -0.8b}

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