4X(X+Y)+5X(2X+Y)=

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Solution for 4X(X+Y)+5X(2X+Y)= equation: 


Simplifying
4X(X + Y) + 5X(2X + Y) = 0
(X * 4X + Y * 4X) + 5X(2X + Y) = 0

Reorder the terms:
(4XY + 4X2) + 5X(2X + Y) = 0
(4XY + 4X2) + 5X(2X + Y) = 0
4XY + 4X2 + (2X * 5X + Y * 5X) = 0

Reorder the terms:
4XY + 4X2 + (5XY + 10X2) = 0
4XY + 4X2 + (5XY + 10X2) = 0

Reorder the terms:
4XY + 5XY + 4X2 + 10X2 = 0

Combine like terms: 4XY + 5XY = 9XY
9XY + 4X2 + 10X2 = 0

Combine like terms: 4X2 + 10X2 = 14X2
9XY + 14X2 = 0

Solving
9XY + 14X2 = 0

Solving for variable 'X'.

Factor out the Greatest Common Factor (GCF), 'X'.
X(9Y + 14X) = 0


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 '(9Y + 14X)' equal to zero and attempt to solve:

Simplifying
9Y + 14X = 0

Reorder the terms:
14X + 9Y = 0

Solving
14X + 9Y = 0

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

Add '-9Y' to each side of the equation.
14X + 9Y + -9Y = 0 + -9Y

Combine like terms: 9Y + -9Y = 0
14X + 0 = 0 + -9Y
14X = 0 + -9Y
Remove the zero:
14X = -9Y

Divide each side by '14'.
X = -0.6428571429Y

Simplifying
X = -0.6428571429Y
Solution
X = {0, -0.6428571429Y}

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