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

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

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

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

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

Reorder the terms:
(-4ab + 5ab + a2 + -20b2) = 0

Combine like terms: -4ab + 5ab = 1ab
(1ab + a2 + -20b2) = 0

Solving
1ab + a2 + -20b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -4b)(a + 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 '(a + 5b)' equal to zero and attempt to solve:

Simplifying
a + 5b = 0

Solving
a + 5b = 0

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

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

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

Simplifying
a = -5b
Solution
a = {4b, -5b}