(a-4b)(6a-5b)=

Solution for (a-4b)(6a-5b)= equation:

Simplifying
(a + -4b)(6a + -5b) = 0

Multiply (a + -4b) * (6a + -5b)
(a(6a + -5b) + -4b * (6a + -5b)) = 0
((6a * a + -5b * a) + -4b * (6a + -5b)) = 0

Reorder the terms:
((-5ab + 6a2) + -4b * (6a + -5b)) = 0
((-5ab + 6a2) + -4b * (6a + -5b)) = 0
(-5ab + 6a2 + (6a * -4b + -5b * -4b)) = 0
(-5ab + 6a2 + (-24ab + 20b2)) = 0

Reorder the terms:
(-5ab + -24ab + 6a2 + 20b2) = 0

Combine like terms: -5ab + -24ab = -29ab
(-29ab + 6a2 + 20b2) = 0

Solving
-29ab + 6a2 + 20b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -4b)(6a + -5b) = 0

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

Simplifying
a + -4b = 0

Solving
a + -4b = 0

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

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

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

Simplifying
a = 4b
Subproblem 2
Set the factor '(6a + -5b)' equal to zero and attempt to solve:

Simplifying
6a + -5b = 0

Solving
6a + -5b = 0

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

Add '5b' to each side of the equation.
6a + -5b + 5b = 0 + 5b

Combine like terms: -5b + 5b = 0
6a + 0 = 0 + 5b
6a = 0 + 5b
Remove the zero:
6a = 5b

Divide each side by '6'.
a = 0.8333333333b

Simplifying
a = 0.8333333333b
Solution
a = {4b, 0.8333333333b}