(3a+3b)(3a-3b)(9a^2+b^2)=

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Solution for (3a+3b)(3a-3b)(9a^2+b^2)= equation: 


Simplifying
(3a + 3b)(3a + -3b)(9a2 + b2) = 0

Multiply (3a + 3b) * (3a + -3b)
(3a * (3a + -3b) + 3b * (3a + -3b))(9a2 + b2) = 0
((3a * 3a + -3b * 3a) + 3b * (3a + -3b))(9a2 + b2) = 0

Reorder the terms:
((-9ab + 9a2) + 3b * (3a + -3b))(9a2 + b2) = 0
((-9ab + 9a2) + 3b * (3a + -3b))(9a2 + b2) = 0
(-9ab + 9a2 + (3a * 3b + -3b * 3b))(9a2 + b2) = 0
(-9ab + 9a2 + (9ab + -9b2))(9a2 + b2) = 0

Reorder the terms:
(-9ab + 9ab + 9a2 + -9b2)(9a2 + b2) = 0

Combine like terms: -9ab + 9ab = 0
(0 + 9a2 + -9b2)(9a2 + b2) = 0
(9a2 + -9b2)(9a2 + b2) = 0

Multiply (9a2 + -9b2) * (9a2 + b2)
(9a2 * (9a2 + b2) + -9b2 * (9a2 + b2)) = 0
((9a2 * 9a2 + b2 * 9a2) + -9b2 * (9a2 + b2)) = 0

Reorder the terms:
((9a2b2 + 81a4) + -9b2 * (9a2 + b2)) = 0
((9a2b2 + 81a4) + -9b2 * (9a2 + b2)) = 0
(9a2b2 + 81a4 + (9a2 * -9b2 + b2 * -9b2)) = 0
(9a2b2 + 81a4 + (-81a2b2 + -9b4)) = 0

Reorder the terms:
(9a2b2 + -81a2b2 + 81a4 + -9b4) = 0

Combine like terms: 9a2b2 + -81a2b2 = -72a2b2
(-72a2b2 + 81a4 + -9b4) = 0

Solving
-72a2b2 + 81a4 + -9b4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '9'.
9(-8a2b2 + 9a4 + -1b4) = 0

Factor a trinomial.
9((a2 + -1b2)(9a2 + b2)) = 0

Factor a difference between two squares.
9(((a + b)(a + -1b))(9a2 + b2)) = 0

Ignore the factor 9.

Subproblem 1
Set the factor '(9a2 + b2)' equal to zero and attempt to solve:

Simplifying
9a2 + b2 = 0

Solving
9a2 + b2 = 0

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

Add '-1b2' to each side of the equation.
9a2 + b2 + -1b2 = 0 + -1b2

Combine like terms: b2 + -1b2 = 0
9a2 + 0 = 0 + -1b2
9a2 = 0 + -1b2
Remove the zero:
9a2 = -1b2

Divide each side by '9'.
a2 = -0.1111111111b2

Simplifying
a2 = -0.1111111111b2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

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

Simplifying
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 '(a + -1b)' equal to zero and attempt to solve:

Simplifying
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 = {-1b, b}

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