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

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

Simplifying
(5a + 3b)(4a + -1b) = 0

Multiply (5a + 3b) * (4a + -1b)
(5a * (4a + -1b) + 3b * (4a + -1b)) = 0
((4a * 5a + -1b * 5a) + 3b * (4a + -1b)) = 0

Reorder the terms:
((-5ab + 20a2) + 3b * (4a + -1b)) = 0
((-5ab + 20a2) + 3b * (4a + -1b)) = 0
(-5ab + 20a2 + (4a * 3b + -1b * 3b)) = 0
(-5ab + 20a2 + (12ab + -3b2)) = 0

Reorder the terms:
(-5ab + 12ab + 20a2 + -3b2) = 0

Combine like terms: -5ab + 12ab = 7ab
(7ab + 20a2 + -3b2) = 0

Solving
7ab + 20a2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(4a + -1b)(5a + 3b) = 0

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

Simplifying
4a + -1b = 0

Solving
4a + -1b = 0

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

Add 'b' to each side of the equation.
4a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
4a + 0 = 0 + b
4a = 0 + b
Remove the zero:
4a = b

Divide each side by '4'.
a = 0.25b

Simplifying
a = 0.25b
Subproblem 2
Set the factor '(5a + 3b)' equal to zero and attempt to solve:

Simplifying
5a + 3b = 0

Solving
5a + 3b = 0

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

Add '-3b' to each side of the equation.
5a + 3b + -3b = 0 + -3b

Combine like terms: 3b + -3b = 0
5a + 0 = 0 + -3b
5a = 0 + -3b
Remove the zero:
5a = -3b

Divide each side by '5'.
a = -0.6b

Simplifying
a = -0.6b
Solution
a = {0.25b, -0.6b}