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

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


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

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

Reorder the terms:
((15ab + 24a2) + -4b * (8a + 5b)) = 0
((15ab + 24a2) + -4b * (8a + 5b)) = 0
(15ab + 24a2 + (8a * -4b + 5b * -4b)) = 0
(15ab + 24a2 + (-32ab + -20b2)) = 0

Reorder the terms:
(15ab + -32ab + 24a2 + -20b2) = 0

Combine like terms: 15ab + -32ab = -17ab
(-17ab + 24a2 + -20b2) = 0

Solving
-17ab + 24a2 + -20b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -4b)(8a + 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 '(8a + 5b)' equal to zero and attempt to solve:

Simplifying
8a + 5b = 0

Solving
8a + 5b = 0

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

Add '-5b' to each side of the equation.
8a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
8a + 0 = 0 + -5b
8a = 0 + -5b
Remove the zero:
8a = -5b

Divide each side by '8'.
a = -0.625b

Simplifying
a = -0.625b
Solution
a = {1.333333333b, -0.625b}

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