(4a-3b)(5a+7b)=

Solution for (4a-3b)(5a+7b)= equation:

Simplifying
(4a + -3b)(5a + 7b) = 0

Multiply (4a + -3b) * (5a + 7b)
(4a * (5a + 7b) + -3b * (5a + 7b)) = 0
((5a * 4a + 7b * 4a) + -3b * (5a + 7b)) = 0

Reorder the terms:
((28ab + 20a2) + -3b * (5a + 7b)) = 0
((28ab + 20a2) + -3b * (5a + 7b)) = 0
(28ab + 20a2 + (5a * -3b + 7b * -3b)) = 0
(28ab + 20a2 + (-15ab + -21b2)) = 0

Reorder the terms:
(28ab + -15ab + 20a2 + -21b2) = 0

Combine like terms: 28ab + -15ab = 13ab
(13ab + 20a2 + -21b2) = 0

Solving
13ab + 20a2 + -21b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -3b)(5a + 7b) = 0

Subproblem 1
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
Subproblem 2
Set the factor '(5a + 7b)' equal to zero and attempt to solve:

Simplifying
5a + 7b = 0

Solving
5a + 7b = 0

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

Add '-7b' to each side of the equation.
5a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
5a + 0 = 0 + -7b
5a = 0 + -7b
Remove the zero:
5a = -7b

Divide each side by '5'.
a = -1.4b

Simplifying
a = -1.4b
Solution
a = {0.75b, -1.4b}