(4a-3b)(2a+6b)=

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

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

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

Reorder the terms:
((24ab + 8a2) + -3b * (2a + 6b)) = 0
((24ab + 8a2) + -3b * (2a + 6b)) = 0
(24ab + 8a2 + (2a * -3b + 6b * -3b)) = 0
(24ab + 8a2 + (-6ab + -18b2)) = 0

Reorder the terms:
(24ab + -6ab + 8a2 + -18b2) = 0

Combine like terms: 24ab + -6ab = 18ab
(18ab + 8a2 + -18b2) = 0

Solving
18ab + 8a2 + -18b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(9ab + 4a2 + -9b2) = 0

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

Ignore the factor 2.
Subproblem 1
Set the factor '(4a + -3b)' equal to zero and attempt to solve:

Simplifying
4a + -3b = 0

Solving
4a + -3b = 0

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

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

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

Divide each side by '4'.
a = 0.75b

Simplifying
a = 0.75b
Subproblem 2
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
Solution
a = {0.75b, -3b}