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

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

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

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

Reorder the terms:
((-32ab + 20a2) + -3b * (5a + -8b)) = 0
((-32ab + 20a2) + -3b * (5a + -8b)) = 0
(-32ab + 20a2 + (5a * -3b + -8b * -3b)) = 0
(-32ab + 20a2 + (-15ab + 24b2)) = 0

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

Combine like terms: -32ab + -15ab = -47ab
(-47ab + 20a2 + 24b2) = 0

Solving
-47ab + 20a2 + 24b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(4a + -3b)' equal to zero and attempt to solve:

Simplifying
4a + -3b = 0

Solving
4a + -3b = 0

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

Add '3b' to each side of the equation.
4a + -3b + 3b = 0 + 3b

Combine like terms: -3b + 3b = 0
4a + 0 = 0 + 3b
4a = 0 + 3b
Remove the zero:
4a = 3b

Divide each side by '4'.
a = 0.75b

Simplifying
a = 0.75b
Solution
a = {1.6b, 0.75b}