(3x^2+4xy-5y^2)+(6x^2-8xy+6y^2)-(2x^2+6xy+9y^2)=

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Solution for (3x^2+4xy-5y^2)+(6x^2-8xy+6y^2)-(2x^2+6xy+9y^2)= equation: 


Simplifying
(3x2 + 4xy + -5y2) + (6x2 + -8xy + 6y2) + -1(2x2 + 6xy + 9y2) = 0

Reorder the terms:
(4xy + 3x2 + -5y2) + (6x2 + -8xy + 6y2) + -1(2x2 + 6xy + 9y2) = 0

Remove parenthesis around (4xy + 3x2 + -5y2)
4xy + 3x2 + -5y2 + (6x2 + -8xy + 6y2) + -1(2x2 + 6xy + 9y2) = 0

Reorder the terms:
4xy + 3x2 + -5y2 + (-8xy + 6x2 + 6y2) + -1(2x2 + 6xy + 9y2) = 0

Remove parenthesis around (-8xy + 6x2 + 6y2)
4xy + 3x2 + -5y2 + -8xy + 6x2 + 6y2 + -1(2x2 + 6xy + 9y2) = 0

Reorder the terms:
4xy + 3x2 + -5y2 + -8xy + 6x2 + 6y2 + -1(6xy + 2x2 + 9y2) = 0
4xy + 3x2 + -5y2 + -8xy + 6x2 + 6y2 + (6xy * -1 + 2x2 * -1 + 9y2 * -1) = 0
4xy + 3x2 + -5y2 + -8xy + 6x2 + 6y2 + (-6xy + -2x2 + -9y2) = 0

Reorder the terms:
4xy + -8xy + -6xy + 3x2 + 6x2 + -2x2 + -5y2 + 6y2 + -9y2 = 0

Combine like terms: 4xy + -8xy = -4xy
-4xy + -6xy + 3x2 + 6x2 + -2x2 + -5y2 + 6y2 + -9y2 = 0

Combine like terms: -4xy + -6xy = -10xy
-10xy + 3x2 + 6x2 + -2x2 + -5y2 + 6y2 + -9y2 = 0

Combine like terms: 3x2 + 6x2 = 9x2
-10xy + 9x2 + -2x2 + -5y2 + 6y2 + -9y2 = 0

Combine like terms: 9x2 + -2x2 = 7x2
-10xy + 7x2 + -5y2 + 6y2 + -9y2 = 0

Combine like terms: -5y2 + 6y2 = 1y2
-10xy + 7x2 + 1y2 + -9y2 = 0

Combine like terms: 1y2 + -9y2 = -8y2
-10xy + 7x2 + -8y2 = 0

Solving
-10xy + 7x2 + -8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(x + -2y)(7x + 4y) = 0


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

Simplifying
x + -2y = 0

Solving
x + -2y = 0

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

Add '2y' to each side of the equation.
x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
x + 0 = 0 + 2y
x = 0 + 2y
Remove the zero:
x = 2y

Simplifying
x = 2y

Subproblem 2
Set the factor '(7x + 4y)' equal to zero and attempt to solve:

Simplifying
7x + 4y = 0

Solving
7x + 4y = 0

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

Add '-4y' to each side of the equation.
7x + 4y + -4y = 0 + -4y

Combine like terms: 4y + -4y = 0
7x + 0 = 0 + -4y
7x = 0 + -4y
Remove the zero:
7x = -4y

Divide each side by '7'.
x = -0.5714285714y

Simplifying
x = -0.5714285714y
Solution
x = {2y, -0.5714285714y}

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