(8a-3b)(2a-5b)=0

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Solution for (8a-3b)(2a-5b)=0 equation: 


Simplifying
(8a + -3b)(2a + -5b) = 0

Multiply (8a + -3b) * (2a + -5b)
(8a * (2a + -5b) + -3b * (2a + -5b)) = 0
((2a * 8a + -5b * 8a) + -3b * (2a + -5b)) = 0

Reorder the terms:
((-40ab + 16a2) + -3b * (2a + -5b)) = 0
((-40ab + 16a2) + -3b * (2a + -5b)) = 0
(-40ab + 16a2 + (2a * -3b + -5b * -3b)) = 0
(-40ab + 16a2 + (-6ab + 15b2)) = 0

Reorder the terms:
(-40ab + -6ab + 16a2 + 15b2) = 0

Combine like terms: -40ab + -6ab = -46ab
(-46ab + 16a2 + 15b2) = 0

Solving
-46ab + 16a2 + 15b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -5b)(8a + -3b) = 0


Subproblem 1
Set the factor '(2a + -5b)' equal to zero and attempt to solve:

Simplifying
2a + -5b = 0

Solving
2a + -5b = 0

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

Add '5b' to each side of the equation.
2a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
2a + 0 = 0 + 5b
2a = 0 + 5b
Remove the zero:
2a = 5b

Divide each side by '2'.
a = 2.5b

Simplifying
a = 2.5b

Subproblem 2
Set the factor '(8a + -3b)' equal to zero and attempt to solve:

Simplifying
8a + -3b = 0

Solving
8a + -3b = 0

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

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

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

Divide each side by '8'.
a = 0.375b

Simplifying
a = 0.375b
Solution
a = {2.5b, 0.375b}

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