(2a+3b)(2a-3b)(4a^2+9b^2)=0

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Solution for (2a+3b)(2a-3b)(4a^2+9b^2)=0 equation: 


Simplifying
(2a + 3b)(2a + -3b)(4a2 + 9b2) = 0

Multiply (2a + 3b) * (2a + -3b)
(2a * (2a + -3b) + 3b * (2a + -3b))(4a2 + 9b2) = 0
((2a * 2a + -3b * 2a) + 3b * (2a + -3b))(4a2 + 9b2) = 0

Reorder the terms:
((-6ab + 4a2) + 3b * (2a + -3b))(4a2 + 9b2) = 0
((-6ab + 4a2) + 3b * (2a + -3b))(4a2 + 9b2) = 0
(-6ab + 4a2 + (2a * 3b + -3b * 3b))(4a2 + 9b2) = 0
(-6ab + 4a2 + (6ab + -9b2))(4a2 + 9b2) = 0

Reorder the terms:
(-6ab + 6ab + 4a2 + -9b2)(4a2 + 9b2) = 0

Combine like terms: -6ab + 6ab = 0
(0 + 4a2 + -9b2)(4a2 + 9b2) = 0
(4a2 + -9b2)(4a2 + 9b2) = 0

Multiply (4a2 + -9b2) * (4a2 + 9b2)
(4a2 * (4a2 + 9b2) + -9b2 * (4a2 + 9b2)) = 0
((4a2 * 4a2 + 9b2 * 4a2) + -9b2 * (4a2 + 9b2)) = 0

Reorder the terms:
((36a2b2 + 16a4) + -9b2 * (4a2 + 9b2)) = 0
((36a2b2 + 16a4) + -9b2 * (4a2 + 9b2)) = 0
(36a2b2 + 16a4 + (4a2 * -9b2 + 9b2 * -9b2)) = 0
(36a2b2 + 16a4 + (-36a2b2 + -81b4)) = 0

Reorder the terms:
(36a2b2 + -36a2b2 + 16a4 + -81b4) = 0

Combine like terms: 36a2b2 + -36a2b2 = 0
(0 + 16a4 + -81b4) = 0
(16a4 + -81b4) = 0

Solving
16a4 + -81b4 = 0

Solving for variable 'a'.

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

Add '81b4' to each side of the equation.
16a4 + -81b4 + 81b4 = 0 + 81b4

Combine like terms: -81b4 + 81b4 = 0
16a4 + 0 = 0 + 81b4
16a4 = 0 + 81b4
Remove the zero:
16a4 = 81b4

Divide each side by '16'.
a4 = 5.0625b4

Simplifying
a4 = 5.0625b4

Combine like terms: 5.0625b4 + -5.0625b4 = 0.0000
a4 + -5.0625b4 = 0.0000

Factor a difference between two squares.
(a2 + 2.25b2)(a2 + -2.25b2) = 0.0000

Factor a difference between two squares.
(a2 + 2.25b2)((a + 1.5b)(a + -1.5b)) = 0.0000


Subproblem 1
Set the factor '(a2 + 2.25b2)' equal to zero and attempt to solve:

Simplifying
a2 + 2.25b2 = 0

Solving
a2 + 2.25b2 = 0

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

Add '-2.25b2' to each side of the equation.
a2 + 2.25b2 + -2.25b2 = 0 + -2.25b2

Combine like terms: 2.25b2 + -2.25b2 = 0.00
a2 + 0.00 = 0 + -2.25b2
a2 = 0 + -2.25b2
Remove the zero:
a2 = -2.25b2

Simplifying
a2 = -2.25b2

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 + 1.5b)' equal to zero and attempt to solve:

Simplifying
a + 1.5b = 0

Solving
a + 1.5b = 0

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

Add '-1.5b' to each side of the equation.
a + 1.5b + -1.5b = 0 + -1.5b

Combine like terms: 1.5b + -1.5b = 0.0
a + 0.0 = 0 + -1.5b
a = 0 + -1.5b
Remove the zero:
a = -1.5b

Simplifying
a = -1.5b

Subproblem 3
Set the factor '(a + -1.5b)' equal to zero and attempt to solve:

Simplifying
a + -1.5b = 0

Solving
a + -1.5b = 0

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

Add '1.5b' to each side of the equation.
a + -1.5b + 1.5b = 0 + 1.5b

Combine like terms: -1.5b + 1.5b = 0.0
a + 0.0 = 0 + 1.5b
a = 0 + 1.5b
Remove the zero:
a = 1.5b

Simplifying
a = 1.5b
Solution
a = {-1.5b, 1.5b}

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