(5a-2b)(3a+b)=

Solution for (5a-2b)(3a+b)= equation:

Simplifying
(5a + -2b)(3a + b) = 0

Multiply (5a + -2b) * (3a + b)
(5a * (3a + b) + -2b * (3a + b)) = 0
((3a * 5a + b * 5a) + -2b * (3a + b)) = 0

Reorder the terms:
((5ab + 15a2) + -2b * (3a + b)) = 0
((5ab + 15a2) + -2b * (3a + b)) = 0
(5ab + 15a2 + (3a * -2b + b * -2b)) = 0
(5ab + 15a2 + (-6ab + -2b2)) = 0

Reorder the terms:
(5ab + -6ab + 15a2 + -2b2) = 0

Combine like terms: 5ab + -6ab = -1ab
(-1ab + 15a2 + -2b2) = 0

Solving
-1ab + 15a2 + -2b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -2b)(3a + b) = 0

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

Simplifying
5a + -2b = 0

Solving
5a + -2b = 0

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

Add '2b' to each side of the equation.
5a + -2b + 2b = 0 + 2b

Combine like terms: -2b + 2b = 0
5a + 0 = 0 + 2b
5a = 0 + 2b
Remove the zero:
5a = 2b

Divide each side by '5'.
a = 0.4b

Simplifying
a = 0.4b
Subproblem 2
Set the factor '(3a + b)' equal to zero and attempt to solve:

Simplifying
3a + b = 0

Solving
3a + b = 0

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

Add '-1b' to each side of the equation.
3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
3a + 0 = 0 + -1b
3a = 0 + -1b
Remove the zero:
3a = -1b

Divide each side by '3'.
a = -0.3333333333b

Simplifying
a = -0.3333333333b
Solution
a = {0.4b, -0.3333333333b}