=10x^2-29xy+10y^2

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Solution for =10x^2-29xy+10y^2 equation: 


Simplifying
0 = 10x2 + -29xy + 10y2

Reorder the terms:
0 = -29xy + 10x2 + 10y2

Solving
0 = -29xy + 10x2 + 10y2

Solving for variable 'x'.
Remove the zero:
29xy + -10x2 + -10y2 = -29xy + 10x2 + 10y2 + 29xy + -10x2 + -10y2

Reorder the terms:
29xy + -10x2 + -10y2 = -29xy + 29xy + 10x2 + -10x2 + 10y2 + -10y2

Combine like terms: -29xy + 29xy = 0
29xy + -10x2 + -10y2 = 0 + 10x2 + -10x2 + 10y2 + -10y2
29xy + -10x2 + -10y2 = 10x2 + -10x2 + 10y2 + -10y2

Combine like terms: 10x2 + -10x2 = 0
29xy + -10x2 + -10y2 = 0 + 10y2 + -10y2
29xy + -10x2 + -10y2 = 10y2 + -10y2

Combine like terms: 10y2 + -10y2 = 0
29xy + -10x2 + -10y2 = 0

Factor a trinomial.
(-5x + 2y)(2x + -5y) = 0


Subproblem 1
Set the factor '(-5x + 2y)' equal to zero and attempt to solve:

Simplifying
-5x + 2y = 0

Solving
-5x + 2y = 0

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

Add '-2y' to each side of the equation.
-5x + 2y + -2y = 0 + -2y

Combine like terms: 2y + -2y = 0
-5x + 0 = 0 + -2y
-5x = 0 + -2y
Remove the zero:
-5x = -2y

Divide each side by '-5'.
x = 0.4y

Simplifying
x = 0.4y

Subproblem 2
Set the factor '(2x + -5y)' equal to zero and attempt to solve:

Simplifying
2x + -5y = 0

Solving
2x + -5y = 0

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

Add '5y' to each side of the equation.
2x + -5y + 5y = 0 + 5y

Combine like terms: -5y + 5y = 0
2x + 0 = 0 + 5y
2x = 0 + 5y
Remove the zero:
2x = 5y

Divide each side by '2'.
x = 2.5y

Simplifying
x = 2.5y
Solution
x = {0.4y, 2.5y}

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