(4a+5b)(8a-7b)=

Solution for (4a+5b)(8a-7b)= equation:

Simplifying
(4a + 5b)(8a + -7b) = 0

Multiply (4a + 5b) * (8a + -7b)
(4a * (8a + -7b) + 5b * (8a + -7b)) = 0
((8a * 4a + -7b * 4a) + 5b * (8a + -7b)) = 0

Reorder the terms:
((-28ab + 32a2) + 5b * (8a + -7b)) = 0
((-28ab + 32a2) + 5b * (8a + -7b)) = 0
(-28ab + 32a2 + (8a * 5b + -7b * 5b)) = 0
(-28ab + 32a2 + (40ab + -35b2)) = 0

Reorder the terms:
(-28ab + 40ab + 32a2 + -35b2) = 0

Combine like terms: -28ab + 40ab = 12ab
(12ab + 32a2 + -35b2) = 0

Solving
12ab + 32a2 + -35b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(8a + -7b)(4a + 5b) = 0

Subproblem 1
Set the factor '(8a + -7b)' equal to zero and attempt to solve:

Simplifying
8a + -7b = 0

Solving
8a + -7b = 0

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

Add '7b' to each side of the equation.
8a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
8a + 0 = 0 + 7b
8a = 0 + 7b
Remove the zero:
8a = 7b

Divide each side by '8'.
a = 0.875b

Simplifying
a = 0.875b
Subproblem 2
Set the factor '(4a + 5b)' equal to zero and attempt to solve:

Simplifying
4a + 5b = 0

Solving
4a + 5b = 0

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

Add '-5b' to each side of the equation.
4a + 5b + -5b = 0 + -5b

Combine like terms: 5b + -5b = 0
4a + 0 = 0 + -5b
4a = 0 + -5b
Remove the zero:
4a = -5b

Divide each side by '4'.
a = -1.25b

Simplifying
a = -1.25b
Solution
a = {0.875b, -1.25b}