2(3a+4b)(6a+7b)=0

Solution for 2(3a+4b)(6a+7b)=0 equation:

Simplifying
2(3a + 4b)(6a + 7b) = 0

Multiply (3a + 4b) * (6a + 7b)
2(3a * (6a + 7b) + 4b * (6a + 7b)) = 0
2((6a * 3a + 7b * 3a) + 4b * (6a + 7b)) = 0

Reorder the terms:
2((21ab + 18a2) + 4b * (6a + 7b)) = 0
2((21ab + 18a2) + 4b * (6a + 7b)) = 0
2(21ab + 18a2 + (6a * 4b + 7b * 4b)) = 0
2(21ab + 18a2 + (24ab + 28b2)) = 0

Reorder the terms:
2(21ab + 24ab + 18a2 + 28b2) = 0

Combine like terms: 21ab + 24ab = 45ab
2(45ab + 18a2 + 28b2) = 0
(45ab * 2 + 18a2 * 2 + 28b2 * 2) = 0
(90ab + 36a2 + 56b2) = 0

Solving
90ab + 36a2 + 56b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(45ab + 18a2 + 28b2) = 0

Factor a trinomial.
2((6a + 7b)(3a + 4b)) = 0

Ignore the factor 2.
Subproblem 1
Set the factor '(6a + 7b)' equal to zero and attempt to solve:

Simplifying
6a + 7b = 0

Solving
6a + 7b = 0

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

Add '-7b' to each side of the equation.
6a + 7b + -7b = 0 + -7b

Combine like terms: 7b + -7b = 0
6a + 0 = 0 + -7b
6a = 0 + -7b
Remove the zero:
6a = -7b

Divide each side by '6'.
a = -1.166666667b

Simplifying
a = -1.166666667b
Subproblem 2
Set the factor '(3a + 4b)' equal to zero and attempt to solve:

Simplifying
3a + 4b = 0

Solving
3a + 4b = 0

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

Add '-4b' to each side of the equation.
3a + 4b + -4b = 0 + -4b

Combine like terms: 4b + -4b = 0
3a + 0 = 0 + -4b
3a = 0 + -4b
Remove the zero:
3a = -4b

Divide each side by '3'.
a = -1.333333333b

Simplifying
a = -1.333333333b
Solution
a = {-1.166666667b, -1.333333333b}