4a^2-3b^2+(2ab+b^2)+(b^2-ab-2a^2)=

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


Simplifying
4a2 + -3b2 + (2ab + b2) + (b2 + -1ab + -2a2) = 0

Remove parenthesis around (2ab + b2)
4a2 + -3b2 + 2ab + b2 + (b2 + -1ab + -2a2) = 0

Reorder the terms:
4a2 + -3b2 + 2ab + b2 + (-1ab + -2a2 + b2) = 0

Remove parenthesis around (-1ab + -2a2 + b2)
4a2 + -3b2 + 2ab + b2 + -1ab + -2a2 + b2 = 0

Reorder the terms:
2ab + -1ab + 4a2 + -2a2 + -3b2 + b2 + b2 = 0

Combine like terms: 2ab + -1ab = 1ab
1ab + 4a2 + -2a2 + -3b2 + b2 + b2 = 0

Combine like terms: 4a2 + -2a2 = 2a2
1ab + 2a2 + -3b2 + b2 + b2 = 0

Combine like terms: -3b2 + b2 = -2b2
1ab + 2a2 + -2b2 + b2 = 0

Combine like terms: -2b2 + b2 = -1b2
1ab + 2a2 + -1b2 = 0

Solving
1ab + 2a2 + -1b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(2a + -1b)(a + b) = 0


Subproblem 1
Set the factor '(2a + -1b)' equal to zero and attempt to solve:

Simplifying
2a + -1b = 0

Solving
2a + -1b = 0

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

Add 'b' to each side of the equation.
2a + -1b + b = 0 + b

Combine like terms: -1b + b = 0
2a + 0 = 0 + b
2a = 0 + b
Remove the zero:
2a = b

Divide each side by '2'.
a = 0.5b

Simplifying
a = 0.5b

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

Simplifying
a + b = 0

Solving
a + b = 0

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

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

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

Simplifying
a = -1b
Solution
a = {0.5b, -1b}

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