(x+y)(x+y)-6(x+h)=0

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Solution for (x+y)(x+y)-6(x+h)=0 equation: 


Simplifying
(x + y)(x + y) + -6(x + h) = 0

Multiply (x + y) * (x + y)
(x(x + y) + y(x + y)) + -6(x + h) = 0
((x * x + y * x) + y(x + y)) + -6(x + h) = 0

Reorder the terms:
((xy + x2) + y(x + y)) + -6(x + h) = 0
((xy + x2) + y(x + y)) + -6(x + h) = 0
(xy + x2 + (x * y + y * y)) + -6(x + h) = 0
(xy + x2 + (xy + y2)) + -6(x + h) = 0

Reorder the terms:
(xy + xy + x2 + y2) + -6(x + h) = 0

Combine like terms: xy + xy = 2xy
(2xy + x2 + y2) + -6(x + h) = 0

Reorder the terms:
2xy + x2 + y2 + -6(h + x) = 0
2xy + x2 + y2 + (h * -6 + x * -6) = 0
2xy + x2 + y2 + (-6h + -6x) = 0

Reorder the terms:
-6h + -6x + 2xy + x2 + y2 = 0

Solving
-6h + -6x + 2xy + x2 + y2 = 0

Solving for variable 'h'.

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

Add '6x' to each side of the equation.
-6h + -6x + 2xy + x2 + 6x + y2 = 0 + 6x

Reorder the terms:
-6h + -6x + 6x + 2xy + x2 + y2 = 0 + 6x

Combine like terms: -6x + 6x = 0
-6h + 0 + 2xy + x2 + y2 = 0 + 6x
-6h + 2xy + x2 + y2 = 0 + 6x
Remove the zero:
-6h + 2xy + x2 + y2 = 6x

Add '-2xy' to each side of the equation.
-6h + 2xy + x2 + -2xy + y2 = 6x + -2xy

Reorder the terms:
-6h + 2xy + -2xy + x2 + y2 = 6x + -2xy

Combine like terms: 2xy + -2xy = 0
-6h + 0 + x2 + y2 = 6x + -2xy
-6h + x2 + y2 = 6x + -2xy

Add '-1x2' to each side of the equation.
-6h + x2 + -1x2 + y2 = 6x + -2xy + -1x2

Combine like terms: x2 + -1x2 = 0
-6h + 0 + y2 = 6x + -2xy + -1x2
-6h + y2 = 6x + -2xy + -1x2

Add '-1y2' to each side of the equation.
-6h + y2 + -1y2 = 6x + -2xy + -1x2 + -1y2

Combine like terms: y2 + -1y2 = 0
-6h + 0 = 6x + -2xy + -1x2 + -1y2
-6h = 6x + -2xy + -1x2 + -1y2

Divide each side by '-6'.
h = -1x + 0.3333333333xy + 0.1666666667x2 + 0.1666666667y2

Simplifying
h = -1x + 0.3333333333xy + 0.1666666667x2 + 0.1666666667y2

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