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

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

Simplifying
3a(a + b)(a + -1b) = 0

Multiply (a + b) * (a + -1b)
3a(a(a + -1b) + b(a + -1b)) = 0
3a((a * a + -1b * a) + b(a + -1b)) = 0

Reorder the terms:
3a((-1ab + a2) + b(a + -1b)) = 0
3a((-1ab + a2) + b(a + -1b)) = 0
3a(-1ab + a2 + (a * b + -1b * b)) = 0
3a(-1ab + a2 + (ab + -1b2)) = 0

Reorder the terms:
3a(-1ab + ab + a2 + -1b2) = 0

Combine like terms: -1ab + ab = 0
3a(0 + a2 + -1b2) = 0
3a(a2 + -1b2) = 0
(a2 * 3a + -1b2 * 3a) = 0

Reorder the terms:
(-3ab2 + 3a3) = 0
(-3ab2 + 3a3) = 0

Solving
-3ab2 + 3a3 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '3a'.
3a(-1b2 + a2) = 0

Factor a difference between two squares.
3a((b + a)(-1b + a)) = 0

Ignore the factor 3.
Subproblem 1
Set the factor 'a' equal to zero and attempt to solve:

Simplifying
a = 0

Solving
a = 0

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

Simplifying
a = 0
Subproblem 2
Set the factor '(b + a)' equal to zero and attempt to solve:

Simplifying
b + a = 0

Reorder the terms:
a + b = 0

Solving
a + b = 0

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

Add '-1b' to each side of the equation.
a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
a + 0 = 0 + -1b
a = 0 + -1b
Remove the zero:
a = -1b

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

Simplifying
-1b + a = 0

Reorder the terms:
a + -1b = 0

Solving
a + -1b = 0

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

Add 'b' to each side of the equation.
a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
a + 0 = 0 + b
a = 0 + b
Remove the zero:
a = b

Simplifying
a = b
Solution
a = {0, -1b, b}