(2X+Y)(4X-3Y)=

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Solution for (2X+Y)(4X-3Y)= equation: 


Simplifying
(2X + Y)(4X + -3Y) = 0

Multiply (2X + Y) * (4X + -3Y)
(2X * (4X + -3Y) + Y(4X + -3Y)) = 0
((4X * 2X + -3Y * 2X) + Y(4X + -3Y)) = 0

Reorder the terms:
((-6XY + 8X2) + Y(4X + -3Y)) = 0
((-6XY + 8X2) + Y(4X + -3Y)) = 0
(-6XY + 8X2 + (4X * Y + -3Y * Y)) = 0
(-6XY + 8X2 + (4XY + -3Y2)) = 0

Reorder the terms:
(-6XY + 4XY + 8X2 + -3Y2) = 0

Combine like terms: -6XY + 4XY = -2XY
(-2XY + 8X2 + -3Y2) = 0

Solving
-2XY + 8X2 + -3Y2 = 0

Solving for variable 'X'.

Factor a trinomial.
(4X + -3Y)(2X + Y) = 0


Subproblem 1
Set the factor '(4X + -3Y)' equal to zero and attempt to solve:

Simplifying
4X + -3Y = 0

Solving
4X + -3Y = 0

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

Add '3Y' to each side of the equation.
4X + -3Y + 3Y = 0 + 3Y

Combine like terms: -3Y + 3Y = 0
4X + 0 = 0 + 3Y
4X = 0 + 3Y
Remove the zero:
4X = 3Y

Divide each side by '4'.
X = 0.75Y

Simplifying
X = 0.75Y

Subproblem 2
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
Solution
X = {0.75Y, -0.5Y}

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