12x^2-10xy-8y^2=0

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Solution for 12x^2-10xy-8y^2=0 equation:


Simplifying
12x2 + -10xy + -8y2 = 0

Reorder the terms:
-10xy + 12x2 + -8y2 = 0

Solving
-10xy + 12x2 + -8y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '2'.
2(-5xy + 6x2 + -4y2) = 0

Factor a trinomial.
2((3x + -4y)(2x + y)) = 0

Ignore the factor 2.

Subproblem 1

Set the factor '(3x + -4y)' equal to zero and attempt to solve: Simplifying 3x + -4y = 0 Solving 3x + -4y = 0 Move all terms containing x to the left, all other terms to the right. Add '4y' to each side of the equation. 3x + -4y + 4y = 0 + 4y Combine like terms: -4y + 4y = 0 3x + 0 = 0 + 4y 3x = 0 + 4y Remove the zero: 3x = 4y Divide each side by '3'. x = 1.333333333y Simplifying x = 1.333333333y

Subproblem 2

Set the factor '(2x + y)' equal to zero and attempt to solve: Simplifying 2x + y = 0 Solving 2x + y = 0 Move all terms containing x to the left, all other terms to the right. Add '-1y' to each side of the equation. 2x + y + -1y = 0 + -1y Combine like terms: y + -1y = 0 2x + 0 = 0 + -1y 2x = 0 + -1y Remove the zero: 2x = -1y Divide each side by '2'. x = -0.5y Simplifying x = -0.5y

Solution

x = {1.333333333y, -0.5y}

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