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

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


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

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

Reorder the terms:
((5ab + 10a2) + -3b * (2a + b)) = 0
((5ab + 10a2) + -3b * (2a + b)) = 0
(5ab + 10a2 + (2a * -3b + b * -3b)) = 0
(5ab + 10a2 + (-6ab + -3b2)) = 0

Reorder the terms:
(5ab + -6ab + 10a2 + -3b2) = 0

Combine like terms: 5ab + -6ab = -1ab
(-1ab + 10a2 + -3b2) = 0

Solving
-1ab + 10a2 + -3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(5a + -3b)(2a + 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 '(2a + b)' equal to zero and attempt to solve:

Simplifying
2a + b = 0

Solving
2a + b = 0

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

Add '-1b' to each side of the equation.
2a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
2a + 0 = 0 + -1b
2a = 0 + -1b
Remove the zero:
2a = -1b

Divide each side by '2'.
a = -0.5b

Simplifying
a = -0.5b
Solution
a = {0.6b, -0.5b}

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