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

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Solution for (3a-4b)(5a+8b)=0 equation: 


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

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

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

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

Combine like terms: 24ab + -20ab = 4ab
(4ab + 15a2 + -32b2) = 0

Solving
4ab + 15a2 + -32b2 = 0

Solving for variable 'a'.

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

Simplifying
5a + 8b = 0

Solving
5a + 8b = 0

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

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

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

Divide each side by '5'.
a = -1.6b

Simplifying
a = -1.6b
Solution
a = {1.333333333b, -1.6b}

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