(2a+8b)(3a-7b)=0

Solution for (2a+8b)(3a-7b)=0 equation:

Simplifying
(2a + 8b)(3a + -7b) = 0

Multiply (2a + 8b) * (3a + -7b)
(2a * (3a + -7b) + 8b * (3a + -7b)) = 0
((3a * 2a + -7b * 2a) + 8b * (3a + -7b)) = 0

Reorder the terms:
((-14ab + 6a2) + 8b * (3a + -7b)) = 0
((-14ab + 6a2) + 8b * (3a + -7b)) = 0
(-14ab + 6a2 + (3a * 8b + -7b * 8b)) = 0
(-14ab + 6a2 + (24ab + -56b2)) = 0

Reorder the terms:
(-14ab + 24ab + 6a2 + -56b2) = 0

Combine like terms: -14ab + 24ab = 10ab
(10ab + 6a2 + -56b2) = 0

Solving
10ab + 6a2 + -56b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(5ab + 3a2 + -28b2) = 0

Factor a trinomial.
2((3a + -7b)(a + 4b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(3a + -7b)' equal to zero and attempt to solve:

Simplifying
3a + -7b = 0

Solving
3a + -7b = 0

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

Add '7b' to each side of the equation.
3a + -7b + 7b = 0 + 7b

Combine like terms: -7b + 7b = 0
3a + 0 = 0 + 7b
3a = 0 + 7b
Remove the zero:
3a = 7b

Divide each side by '3'.
a = 2.333333333b

Simplifying
a = 2.333333333b
Subproblem 2
Set the factor '(a + 4b)' equal to zero and attempt to solve:

Simplifying
a + 4b = 0

Solving
a + 4b = 0

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

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

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

Simplifying
a = -4b
Solution
a = {2.333333333b, -4b}