2x(2y+3)+x(4y+6)=

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Solution for 2x(2y+3)+x(4y+6)= equation: 


Simplifying
2x(2y + 3) + x(4y + 6) = 0

Reorder the terms:
2x(3 + 2y) + x(4y + 6) = 0
(3 * 2x + 2y * 2x) + x(4y + 6) = 0
(6x + 4xy) + x(4y + 6) = 0

Reorder the terms:
6x + 4xy + x(6 + 4y) = 0
6x + 4xy + (6 * x + 4y * x) = 0
6x + 4xy + (6x + 4xy) = 0

Reorder the terms:
6x + 6x + 4xy + 4xy = 0

Combine like terms: 6x + 6x = 12x
12x + 4xy + 4xy = 0

Combine like terms: 4xy + 4xy = 8xy
12x + 8xy = 0

Solving
12x + 8xy = 0

Solving for variable 'x'.

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

Factor out the Greatest Common Factor (GCF), '4x'.
4x(3 + 2y) = 0

Ignore the factor 4.

Subproblem 1
Set the factor 'x' equal to zero and attempt to solve:

Simplifying
x = 0

Solving
x = 0

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

Simplifying
x = 0

Subproblem 2
Set the factor '(3 + 2y)' equal to zero and attempt to solve:

Simplifying
3 + 2y = 0

Solving
3 + 2y = 0

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

Add '-3' to each side of the equation.
3 + -3 + 2y = 0 + -3

Combine like terms: 3 + -3 = 0
0 + 2y = 0 + -3
2y = 0 + -3

Combine like terms: 0 + -3 = -3
2y = -3

Add '-2y' to each side of the equation.
2y + -2y = -3 + -2y

Combine like terms: 2y + -2y = 0
0 = -3 + -2y

Simplifying
0 = -3 + -2y

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.
Solution
x = {0}

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