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

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


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

Reorder the terms for easier multiplication:
(4 * 4a * a + -3b * 3b)(4a * 4a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply 4 * 4
(16a * a + -3b * 3b)(4a * 4a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply a * a
(16a2 + -3b * 3b)(4a * 4a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms for easier multiplication:
(16a2 + -3 * 3b * b)(4a * 4a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply -3 * 3
(16a2 + -9b * b)(4a * 4a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply b * b
(16a2 + -9b2)(4a * 4a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms for easier multiplication:
(16a2 + -9b2)(4 * 4a * a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply 4 * 4
(16a2 + -9b2)(16a * a + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply a * a
(16a2 + -9b2)(16a2 + -3b * 3b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms for easier multiplication:
(16a2 + -9b2)(16a2 + -3 * 3b * b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply -3 * 3
(16a2 + -9b2)(16a2 + -9b * b) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply b * b
(16a2 + -9b2)(16a2 + -9b2) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply (16a2 + -9b2) * (16a2 + -9b2)
(16a2 * (16a2 + -9b2) + -9b2 * (16a2 + -9b2)) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0
((16a2 * 16a2 + -9b2 * 16a2) + -9b2 * (16a2 + -9b2)) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms:
((-144a2b2 + 256a4) + -9b2 * (16a2 + -9b2)) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0
((-144a2b2 + 256a4) + -9b2 * (16a2 + -9b2)) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0
(-144a2b2 + 256a4 + (16a2 * -9b2 + -9b2 * -9b2)) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0
(-144a2b2 + 256a4 + (-144a2b2 + 81b4)) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms:
(-144a2b2 + -144a2b2 + 256a4 + 81b4) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Combine like terms: -144a2b2 + -144a2b2 = -288a2b2
(-288a2b2 + 256a4 + 81b4) + (3b * 3b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms for easier multiplication:
-288a2b2 + 256a4 + 81b4 + (3 * 3b * b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply 3 * 3
-288a2b2 + 256a4 + 81b4 + (9b * b + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Multiply b * b
-288a2b2 + 256a4 + 81b4 + (9b2 + -4a * 4a)(3b * 3b + -4a * 4a) = 0

Reorder the terms for easier multiplication:
-288a2b2 + 256a4 + 81b4 + (9b2 + -4 * 4a * a)(3b * 3b + -4a * 4a) = 0

Multiply -4 * 4
-288a2b2 + 256a4 + 81b4 + (9b2 + -16a * a)(3b * 3b + -4a * 4a) = 0

Multiply a * a
-288a2b2 + 256a4 + 81b4 + (9b2 + -16a2)(3b * 3b + -4a * 4a) = 0

Reorder the terms:
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(3b * 3b + -4a * 4a) = 0

Reorder the terms for easier multiplication:
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(3 * 3b * b + -4a * 4a) = 0

Multiply 3 * 3
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(9b * b + -4a * 4a) = 0

Multiply b * b
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(9b2 + -4a * 4a) = 0

Reorder the terms for easier multiplication:
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(9b2 + -4 * 4a * a) = 0

Multiply -4 * 4
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(9b2 + -16a * a) = 0

Multiply a * a
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(9b2 + -16a2) = 0

Reorder the terms:
-288a2b2 + 256a4 + 81b4 + (-16a2 + 9b2)(-16a2 + 9b2) = 0

Multiply (-16a2 + 9b2) * (-16a2 + 9b2)
-288a2b2 + 256a4 + 81b4 + (-16a2 * (-16a2 + 9b2) + 9b2 * (-16a2 + 9b2)) = 0
-288a2b2 + 256a4 + 81b4 + ((-16a2 * -16a2 + 9b2 * -16a2) + 9b2 * (-16a2 + 9b2)) = 0

Reorder the terms:
-288a2b2 + 256a4 + 81b4 + ((-144a2b2 + 256a4) + 9b2 * (-16a2 + 9b2)) = 0
-288a2b2 + 256a4 + 81b4 + ((-144a2b2 + 256a4) + 9b2 * (-16a2 + 9b2)) = 0
-288a2b2 + 256a4 + 81b4 + (-144a2b2 + 256a4 + (-16a2 * 9b2 + 9b2 * 9b2)) = 0
-288a2b2 + 256a4 + 81b4 + (-144a2b2 + 256a4 + (-144a2b2 + 81b4)) = 0

Reorder the terms:
-288a2b2 + 256a4 + 81b4 + (-144a2b2 + -144a2b2 + 256a4 + 81b4) = 0

Combine like terms: -144a2b2 + -144a2b2 = -288a2b2
-288a2b2 + 256a4 + 81b4 + (-288a2b2 + 256a4 + 81b4) = 0

Reorder the terms:
-288a2b2 + -288a2b2 + 256a4 + 256a4 + 81b4 + 81b4 = 0

Combine like terms: -288a2b2 + -288a2b2 = -576a2b2
-576a2b2 + 256a4 + 256a4 + 81b4 + 81b4 = 0

Combine like terms: 256a4 + 256a4 = 512a4
-576a2b2 + 512a4 + 81b4 + 81b4 = 0

Combine like terms: 81b4 + 81b4 = 162b4
-576a2b2 + 512a4 + 162b4 = 0

Solving
-576a2b2 + 512a4 + 162b4 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-288a2b2 + 256a4 + 81b4) = 0

Factor a trinomial.
2((16a2 + -9b2)(16a2 + -9b2)) = 0

Factor a difference between two squares.
2(((4a + 3b)(4a + -3b))(16a2 + -9b2)) = 0

Factor a difference between two squares.
2(((4a + 3b)(4a + -3b))(4a + 3b)(4a + -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 '(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 3
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 4
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
Solution
a = {-0.75b, 0.75b, -0.75b, 0.75b}

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