(3ab-2)(a+3b)+(2a^2+5b)(b+1)+(a-1)(9b^2-2a)-2b(9ab-2b)=0

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Solution for (3ab-2)(a+3b)+(2a^2+5b)(b+1)+(a-1)(9b^2-2a)-2b(9ab-2b)=0 equation: 


Simplifying
(3ab + -2)(a + 3b) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Reorder the terms:
(-2 + 3ab)(a + 3b) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Multiply (-2 + 3ab) * (a + 3b)
(-2(a + 3b) + 3ab * (a + 3b)) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
((a * -2 + 3b * -2) + 3ab * (a + 3b)) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
((-2a + -6b) + 3ab * (a + 3b)) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
(-2a + -6b + (a * 3ab + 3b * 3ab)) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Reorder the terms:
(-2a + -6b + (9ab2 + 3a2b)) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
(-2a + -6b + (9ab2 + 3a2b)) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Reorder the terms:
(-2a + 9ab2 + 3a2b + -6b) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
(-2a + 9ab2 + 3a2b + -6b) + (2a2 + 5b)(b + 1) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Reorder the terms:
-2a + 9ab2 + 3a2b + -6b + (2a2 + 5b)(1 + b) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Multiply (2a2 + 5b) * (1 + b)
-2a + 9ab2 + 3a2b + -6b + (2a2 * (1 + b) + 5b * (1 + b)) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + ((1 * 2a2 + b * 2a2) + 5b * (1 + b)) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + ((2a2 + 2a2b) + 5b * (1 + b)) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + (2a2 + 2a2b + (1 * 5b + b * 5b)) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + (2a2 + 2a2b + (5b + 5b2)) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + (2a2 + 2a2b + 5b + 5b2) + (a + -1)(9b2 + -2a) + -2b(9ab + -2b) = 0

Reorder the terms:
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (-1 + a)(9b2 + -2a) + -2b(9ab + -2b) = 0

Reorder the terms:
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (-1 + a)(-2a + 9b2) + -2b(9ab + -2b) = 0

Multiply (-1 + a) * (-2a + 9b2)
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (-1(-2a + 9b2) + a(-2a + 9b2)) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + ((-2a * -1 + 9b2 * -1) + a(-2a + 9b2)) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + ((2a + -9b2) + a(-2a + 9b2)) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (2a + -9b2 + (-2a * a + 9b2 * a)) + -2b(9ab + -2b) = 0

Reorder the terms:
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (2a + -9b2 + (9ab2 + -2a2)) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (2a + -9b2 + (9ab2 + -2a2)) + -2b(9ab + -2b) = 0

Reorder the terms:
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (2a + 9ab2 + -2a2 + -9b2) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + (2a + 9ab2 + -2a2 + -9b2) + -2b(9ab + -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + 2a + 9ab2 + -2a2 + -9b2 + (9ab * -2b + -2b * -2b) = 0
-2a + 9ab2 + 3a2b + -6b + 2a2 + 2a2b + 5b + 5b2 + 2a + 9ab2 + -2a2 + -9b2 + (-18ab2 + 4b2) = 0

Reorder the terms:
-2a + 2a + 9ab2 + 9ab2 + -18ab2 + 2a2 + -2a2 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: -2a + 2a = 0
0 + 9ab2 + 9ab2 + -18ab2 + 2a2 + -2a2 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0
9ab2 + 9ab2 + -18ab2 + 2a2 + -2a2 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: 9ab2 + 9ab2 = 18ab2
18ab2 + -18ab2 + 2a2 + -2a2 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: 18ab2 + -18ab2 = 0
0 + 2a2 + -2a2 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0
2a2 + -2a2 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: 2a2 + -2a2 = 0
0 + 3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0
3a2b + 2a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: 3a2b + 2a2b = 5a2b
5a2b + -6b + 5b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: -6b + 5b = -1b
5a2b + -1b + 5b2 + -9b2 + 4b2 = 0

Combine like terms: 5b2 + -9b2 = -4b2
5a2b + -1b + -4b2 + 4b2 = 0

Combine like terms: -4b2 + 4b2 = 0
5a2b + -1b + 0 = 0
5a2b + -1b = 0

Solving
5a2b + -1b = 0

Solving for variable 'a'.

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

Add 'b' to each side of the equation.
5a2b + -1b + b = 0 + b

Combine like terms: -1b + b = 0
5a2b + 0 = 0 + b
5a2b = 0 + b
Remove the zero:
5a2b = b

Divide each side by '5b'.
a2 = 0.2

Simplifying
a2 = 0.2

Take the square root of each side:
a = {-0.447213596, 0.447213596}

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