(2X+Y)(X+3Y)=

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Solution for (2X+Y)(X+3Y)= equation: 


Simplifying
(2X + Y)(X + 3Y) = 0

Multiply (2X + Y) * (X + 3Y)
(2X * (X + 3Y) + Y(X + 3Y)) = 0
((X * 2X + 3Y * 2X) + Y(X + 3Y)) = 0

Reorder the terms:
((6XY + 2X2) + Y(X + 3Y)) = 0
((6XY + 2X2) + Y(X + 3Y)) = 0
(6XY + 2X2 + (X * Y + 3Y * Y)) = 0
(6XY + 2X2 + (XY + 3Y2)) = 0

Reorder the terms:
(6XY + XY + 2X2 + 3Y2) = 0

Combine like terms: 6XY + XY = 7XY
(7XY + 2X2 + 3Y2) = 0

Solving
7XY + 2X2 + 3Y2 = 0

Solving for variable 'X'.

Factor a trinomial.
(2X + Y)(X + 3Y) = 0


Subproblem 1
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

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

Simplifying
X + 3Y = 0

Solving
X + 3Y = 0

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

Add '-3Y' to each side of the equation.
X + 3Y + -3Y = 0 + -3Y

Combine like terms: 3Y + -3Y = 0
X + 0 = 0 + -3Y
X = 0 + -3Y
Remove the zero:
X = -3Y

Simplifying
X = -3Y
Solution
X = {-0.5Y, -3Y}

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