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

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


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

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

Reorder the terms:
((-24ab + 9a2) + 5b * (3a + -8b)) = 0
((-24ab + 9a2) + 5b * (3a + -8b)) = 0
(-24ab + 9a2 + (3a * 5b + -8b * 5b)) = 0
(-24ab + 9a2 + (15ab + -40b2)) = 0

Reorder the terms:
(-24ab + 15ab + 9a2 + -40b2) = 0

Combine like terms: -24ab + 15ab = -9ab
(-9ab + 9a2 + -40b2) = 0

Solving
-9ab + 9a2 + -40b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(3a + -8b)(3a + 5b) = 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 '(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
Solution
a = {2.666666667b, -1.666666667b}

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