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

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

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

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

Reorder the terms:
((28ab + 4a2) + -5b * (a + 7b)) = 0
((28ab + 4a2) + -5b * (a + 7b)) = 0
(28ab + 4a2 + (a * -5b + 7b * -5b)) = 0
(28ab + 4a2 + (-5ab + -35b2)) = 0

Reorder the terms:
(28ab + -5ab + 4a2 + -35b2) = 0

Combine like terms: 28ab + -5ab = 23ab
(23ab + 4a2 + -35b2) = 0

Solving
23ab + 4a2 + -35b2 = 0

Solving for variable 'a'.

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

Subproblem 1
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
Subproblem 2
Set the factor '(a + 7b)' equal to zero and attempt to solve:

Simplifying
a + 7b = 0

Solving
a + 7b = 0

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

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

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

Simplifying
a = -7b
Solution
a = {1.25b, -7b}