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

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

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

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

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

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

Combine like terms: -3ab + 5ab = 2ab
(2ab + 5a2 + -3b2) = 0

Solving
2ab + 5a2 + -3b2 = 0

Solving for variable 'a'.

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

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {0.6b, -1b}