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

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


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

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

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

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

Combine like terms: -40ab + -9ab = -49ab
(-49ab + 15a2 + 24b2) = 0

Solving
-49ab + 15a2 + 24b2 = 0

Solving for variable 'a'.

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

Simplifying
5a + -3b = 0

Solving
5a + -3b = 0

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

Add '3b' to each side of the equation.
5a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
5a + 0 = 0 + 3b
5a = 0 + 3b
Remove the zero:
5a = 3b

Divide each side by '5'.
a = 0.6b

Simplifying
a = 0.6b
Solution
a = {2.666666667b, 0.6b}

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