(3+b)*(3-b-a-2)+(a-1)*(b-1)=

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Solution for (3+b)*(3-b-a-2)+(a-1)*(b-1)= equation: 


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

Reorder the terms:
(3 + b)(3 + -2 + -1a + -1b) + (a + -1)(b + -1) = 0

Combine like terms: 3 + -2 = 1
(3 + b)(1 + -1a + -1b) + (a + -1)(b + -1) = 0

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

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

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

Combine like terms: -3b + 1b = -2b
(3 + -3a + -1ab + -2b + -1b2) + (a + -1)(b + -1) = 0

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

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

Multiply (-1 + a) * (-1 + b)
3 + -3a + -1ab + -2b + -1b2 + (-1(-1 + b) + a(-1 + b)) = 0
3 + -3a + -1ab + -2b + -1b2 + ((-1 * -1 + b * -1) + a(-1 + b)) = 0
3 + -3a + -1ab + -2b + -1b2 + ((1 + -1b) + a(-1 + b)) = 0
3 + -3a + -1ab + -2b + -1b2 + (1 + -1b + (-1 * a + b * a)) = 0
3 + -3a + -1ab + -2b + -1b2 + (1 + -1b + (-1a + ab)) = 0

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

Reorder the terms:
3 + 1 + -3a + -1a + -1ab + ab + -2b + -1b + -1b2 = 0

Combine like terms: 3 + 1 = 4
4 + -3a + -1a + -1ab + ab + -2b + -1b + -1b2 = 0

Combine like terms: -3a + -1a = -4a
4 + -4a + -1ab + ab + -2b + -1b + -1b2 = 0

Combine like terms: -1ab + ab = 0
4 + -4a + 0 + -2b + -1b + -1b2 = 0
4 + -4a + -2b + -1b + -1b2 = 0

Combine like terms: -2b + -1b = -3b
4 + -4a + -3b + -1b2 = 0

Solving
4 + -4a + -3b + -1b2 = 0

Solving for variable 'a'.

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

Add '-4' to each side of the equation.
4 + -4a + -3b + -4 + -1b2 = 0 + -4

Reorder the terms:
4 + -4 + -4a + -3b + -1b2 = 0 + -4

Combine like terms: 4 + -4 = 0
0 + -4a + -3b + -1b2 = 0 + -4
-4a + -3b + -1b2 = 0 + -4

Combine like terms: 0 + -4 = -4
-4a + -3b + -1b2 = -4

Add '3b' to each side of the equation.
-4a + -3b + 3b + -1b2 = -4 + 3b

Combine like terms: -3b + 3b = 0
-4a + 0 + -1b2 = -4 + 3b
-4a + -1b2 = -4 + 3b

Add 'b2' to each side of the equation.
-4a + -1b2 + b2 = -4 + 3b + b2

Combine like terms: -1b2 + b2 = 0
-4a + 0 = -4 + 3b + b2
-4a = -4 + 3b + b2

Divide each side by '-4'.
a = 1 + -0.75b + -0.25b2

Simplifying
a = 1 + -0.75b + -0.25b2

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