9a*9a-(3a-2b)*(3a-2b)=0

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Solution for 9a*9a-(3a-2b)*(3a-2b)=0 equation: 


Simplifying
9a * 9a + -1(3a + -2b)(3a + -2b) = 0

Reorder the terms for easier multiplication:
9 * 9a * a + -1(3a + -2b)(3a + -2b) = 0

Multiply 9 * 9
81a * a + -1(3a + -2b)(3a + -2b) = 0

Multiply a * a
81a2 + -1(3a + -2b)(3a + -2b) = 0

Multiply (3a + -2b) * (3a + -2b)
81a2 + -1(3a * (3a + -2b) + -2b * (3a + -2b)) = 0
81a2 + -1((3a * 3a + -2b * 3a) + -2b * (3a + -2b)) = 0

Reorder the terms:
81a2 + -1((-6ab + 9a2) + -2b * (3a + -2b)) = 0
81a2 + -1((-6ab + 9a2) + -2b * (3a + -2b)) = 0
81a2 + -1(-6ab + 9a2 + (3a * -2b + -2b * -2b)) = 0
81a2 + -1(-6ab + 9a2 + (-6ab + 4b2)) = 0

Reorder the terms:
81a2 + -1(-6ab + -6ab + 9a2 + 4b2) = 0

Combine like terms: -6ab + -6ab = -12ab
81a2 + -1(-12ab + 9a2 + 4b2) = 0
81a2 + (-12ab * -1 + 9a2 * -1 + 4b2 * -1) = 0
81a2 + (12ab + -9a2 + -4b2) = 0

Reorder the terms:
12ab + 81a2 + -9a2 + -4b2 = 0

Combine like terms: 81a2 + -9a2 = 72a2
12ab + 72a2 + -4b2 = 0

Solving
12ab + 72a2 + -4b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '4'.
4(3ab + 18a2 + -1b2) = 0

Factor a trinomial.
4((6a + -1b)(3a + b)) = 0

Ignore the factor 4.

Subproblem 1
Set the factor '(6a + -1b)' equal to zero and attempt to solve:

Simplifying
6a + -1b = 0

Solving
6a + -1b = 0

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

Add 'b' to each side of the equation.
6a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
6a + 0 = 0 + b
6a = 0 + b
Remove the zero:
6a = b

Divide each side by '6'.
a = 0.1666666667b

Simplifying
a = 0.1666666667b

Subproblem 2
Set the factor '(3a + b)' equal to zero and attempt to solve:

Simplifying
3a + b = 0

Solving
3a + b = 0

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

Add '-1b' to each side of the equation.
3a + b + -1b = 0 + -1b

Combine like terms: b + -1b = 0
3a + 0 = 0 + -1b
3a = 0 + -1b
Remove the zero:
3a = -1b

Divide each side by '3'.
a = -0.3333333333b

Simplifying
a = -0.3333333333b
Solution
a = {0.1666666667b, -0.3333333333b}

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