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

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

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

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

Reorder the terms:
2((-4ab + a2) + 3b * (a + -4b)) = 0
2((-4ab + a2) + 3b * (a + -4b)) = 0
2(-4ab + a2 + (a * 3b + -4b * 3b)) = 0
2(-4ab + a2 + (3ab + -12b2)) = 0

Reorder the terms:
2(-4ab + 3ab + a2 + -12b2) = 0

Combine like terms: -4ab + 3ab = -1ab
2(-1ab + a2 + -12b2) = 0
(-1ab * 2 + a2 * 2 + -12b2 * 2) = 0
(-2ab + 2a2 + -24b2) = 0

Solving
-2ab + 2a2 + -24b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-1ab + a2 + -12b2) = 0

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

Ignore the factor 2.
Subproblem 1
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
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 = {4b, -3b}