(-4a^2+3ab+6b^2)+(-2a^2+2ab-5b^2)=

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Solution for (-4a^2+3ab+6b^2)+(-2a^2+2ab-5b^2)= equation: 


Simplifying
(-4a2 + 3ab + 6b2) + (-2a2 + 2ab + -5b2) = 0

Reorder the terms:
(3ab + -4a2 + 6b2) + (-2a2 + 2ab + -5b2) = 0

Remove parenthesis around (3ab + -4a2 + 6b2)
3ab + -4a2 + 6b2 + (-2a2 + 2ab + -5b2) = 0

Reorder the terms:
3ab + -4a2 + 6b2 + (2ab + -2a2 + -5b2) = 0

Remove parenthesis around (2ab + -2a2 + -5b2)
3ab + -4a2 + 6b2 + 2ab + -2a2 + -5b2 = 0

Reorder the terms:
3ab + 2ab + -4a2 + -2a2 + 6b2 + -5b2 = 0

Combine like terms: 3ab + 2ab = 5ab
5ab + -4a2 + -2a2 + 6b2 + -5b2 = 0

Combine like terms: -4a2 + -2a2 = -6a2
5ab + -6a2 + 6b2 + -5b2 = 0

Combine like terms: 6b2 + -5b2 = 1b2
5ab + -6a2 + 1b2 = 0

Solving
5ab + -6a2 + 1b2 = 0

Solving for variable 'a'.

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


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 '(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
Solution
a = {-0.1666666667b, b}

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