(2a^2+3ab-4b^2)-(a^2+1ab-1b^2)=0

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Solution for (2a^2+3ab-4b^2)-(a^2+1ab-1b^2)=0 equation: 


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

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

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

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

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

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

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

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

Solving
2ab + 1a2 + -3b2 = 0

Solving for variable 'a'.

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


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

Simplifying
a + -1b = 0

Solving
a + -1b = 0

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

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

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

Simplifying
a = b

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

Simplifying
a + 3b = 0

Solving
a + 3b = 0

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

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

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

Simplifying
a = -3b
Solution
a = {b, -3b}

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