6(x+y)y+3(x+3)=

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Solution for 6(x+y)y+3(x+3)= equation: 


Simplifying
6(x + y) * y + 3(x + 3) = 0

Reorder the terms for easier multiplication:
6y(x + y) + 3(x + 3) = 0
(x * 6y + y * 6y) + 3(x + 3) = 0
(6xy + 6y2) + 3(x + 3) = 0

Reorder the terms:
6xy + 6y2 + 3(3 + x) = 0
6xy + 6y2 + (3 * 3 + x * 3) = 0
6xy + 6y2 + (9 + 3x) = 0

Reorder the terms:
9 + 3x + 6xy + 6y2 = 0

Solving
9 + 3x + 6xy + 6y2 = 0

Solving for variable 'x'.

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

Add '-9' to each side of the equation.
9 + 3x + 6xy + -9 + 6y2 = 0 + -9

Reorder the terms:
9 + -9 + 3x + 6xy + 6y2 = 0 + -9

Combine like terms: 9 + -9 = 0
0 + 3x + 6xy + 6y2 = 0 + -9
3x + 6xy + 6y2 = 0 + -9

Combine like terms: 0 + -9 = -9
3x + 6xy + 6y2 = -9

Add '-6y2' to each side of the equation.
3x + 6xy + 6y2 + -6y2 = -9 + -6y2

Combine like terms: 6y2 + -6y2 = 0
3x + 6xy + 0 = -9 + -6y2
3x + 6xy = -9 + -6y2

Reorder the terms:
9 + 3x + 6xy + 6y2 = -9 + -6y2 + 9 + 6y2

Reorder the terms:
9 + 3x + 6xy + 6y2 = -9 + 9 + -6y2 + 6y2

Combine like terms: -9 + 9 = 0
9 + 3x + 6xy + 6y2 = 0 + -6y2 + 6y2
9 + 3x + 6xy + 6y2 = -6y2 + 6y2

Combine like terms: -6y2 + 6y2 = 0
9 + 3x + 6xy + 6y2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(3 + x + 2xy + 2y2) = 0

Ignore the factor 3.

Subproblem 1
Set the factor '(3 + x + 2xy + 2y2)' equal to zero and attempt to solve:

Simplifying
3 + x + 2xy + 2y2 = 0

Solving
3 + x + 2xy + 2y2 = 0

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

Add '-3' to each side of the equation.
3 + x + 2xy + -3 + 2y2 = 0 + -3

Reorder the terms:
3 + -3 + x + 2xy + 2y2 = 0 + -3

Combine like terms: 3 + -3 = 0
0 + x + 2xy + 2y2 = 0 + -3
x + 2xy + 2y2 = 0 + -3

Combine like terms: 0 + -3 = -3
x + 2xy + 2y2 = -3

Add '-2y2' to each side of the equation.
x + 2xy + 2y2 + -2y2 = -3 + -2y2

Combine like terms: 2y2 + -2y2 = 0
x + 2xy + 0 = -3 + -2y2
x + 2xy = -3 + -2y2

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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