3y^2-2x^2+5y^2+7x^2+x+x-6x^2=

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Solution for 3y^2-2x^2+5y^2+7x^2+x+x-6x^2= equation:


Simplifying
3y2 + -2x2 + 5y2 + 7x2 + x + x + -6x2 = 0

Reorder the terms:
x + x + -2x2 + 7x2 + -6x2 + 3y2 + 5y2 = 0

Combine like terms: x + x = 2x
2x + -2x2 + 7x2 + -6x2 + 3y2 + 5y2 = 0

Combine like terms: -2x2 + 7x2 = 5x2
2x + 5x2 + -6x2 + 3y2 + 5y2 = 0

Combine like terms: 5x2 + -6x2 = -1x2
2x + -1x2 + 3y2 + 5y2 = 0

Combine like terms: 3y2 + 5y2 = 8y2
2x + -1x2 + 8y2 = 0

Solving
2x + -1x2 + 8y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-1x + -2y)(x + -4y) = 0

Subproblem 1

Set the factor '(-1x + -2y)' equal to zero and attempt to solve: Simplifying -1x + -2y = 0 Solving -1x + -2y = 0 Move all terms containing x to the left, all other terms to the right. Add '2y' to each side of the equation. -1x + -2y + 2y = 0 + 2y Combine like terms: -2y + 2y = 0 -1x + 0 = 0 + 2y -1x = 0 + 2y Remove the zero: -1x = 2y Divide each side by '-1'. x = -2y Simplifying x = -2y

Subproblem 2

Set the factor '(x + -4y)' equal to zero and attempt to solve: Simplifying x + -4y = 0 Solving x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 x + 0 = 0 + 4y x = 0 + 4y Remove the zero: x = 4y Simplifying x = 4y

Solution

x = {-2y, 4y}

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