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

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Solution for (4a+b)(5a-3b)=0 equation: 


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

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

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

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

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

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

Solving for variable 'a'.

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


Subproblem 1
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

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

Simplifying
4a + b = 0

Solving
4a + b = 0

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

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

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

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

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

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