(5a+7b)(a-3b)=0

Solution for (5a+7b)(a-3b)=0 equation:

Simplifying
(5a + 7b)(a + -3b) = 0

Multiply (5a + 7b) * (a + -3b)
(5a * (a + -3b) + 7b * (a + -3b)) = 0
((a * 5a + -3b * 5a) + 7b * (a + -3b)) = 0

Reorder the terms:
((-15ab + 5a2) + 7b * (a + -3b)) = 0
((-15ab + 5a2) + 7b * (a + -3b)) = 0
(-15ab + 5a2 + (a * 7b + -3b * 7b)) = 0
(-15ab + 5a2 + (7ab + -21b2)) = 0

Reorder the terms:
(-15ab + 7ab + 5a2 + -21b2) = 0

Combine like terms: -15ab + 7ab = -8ab
(-8ab + 5a2 + -21b2) = 0

Solving
-8ab + 5a2 + -21b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(a + -3b)(5a + 7b) = 0

Subproblem 1
Set the factor '(a + -3b)' equal to zero and attempt to solve:

Simplifying
a + -3b = 0

Solving
a + -3b = 0

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

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

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

Simplifying
a = 3b
Subproblem 2
Set the factor '(5a + 7b)' equal to zero and attempt to solve:

Simplifying
5a + 7b = 0

Solving
5a + 7b = 0

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

Add '-7b' to each side of the equation.
5a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
5a + 0 = 0 + -7b
5a = 0 + -7b
Remove the zero:
5a = -7b

Divide each side by '5'.
a = -1.4b

Simplifying
a = -1.4b
Solution
a = {3b, -1.4b}