(2x+3y)(4x-y)=0

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Solution for (2x+3y)(4x-y)=0 equation: 


Simplifying
(2x + 3y)(4x + -1y) = 0

Multiply (2x + 3y) * (4x + -1y)
(2x * (4x + -1y) + 3y * (4x + -1y)) = 0
((4x * 2x + -1y * 2x) + 3y * (4x + -1y)) = 0

Reorder the terms:
((-2xy + 8x2) + 3y * (4x + -1y)) = 0
((-2xy + 8x2) + 3y * (4x + -1y)) = 0
(-2xy + 8x2 + (4x * 3y + -1y * 3y)) = 0
(-2xy + 8x2 + (12xy + -3y2)) = 0

Reorder the terms:
(-2xy + 12xy + 8x2 + -3y2) = 0

Combine like terms: -2xy + 12xy = 10xy
(10xy + 8x2 + -3y2) = 0

Solving
10xy + 8x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(4x + -1y)(2x + 3y) = 0


Subproblem 1
Set the factor '(4x + -1y)' equal to zero and attempt to solve:

Simplifying
4x + -1y = 0

Solving
4x + -1y = 0

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

Add 'y' to each side of the equation.
4x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
4x + 0 = 0 + y
4x = 0 + y
Remove the zero:
4x = y

Divide each side by '4'.
x = 0.25y

Simplifying
x = 0.25y

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

Simplifying
2x + 3y = 0

Solving
2x + 3y = 0

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

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

Combine like terms: 3y + -3y = 0
2x + 0 = 0 + -3y
2x = 0 + -3y
Remove the zero:
2x = -3y

Divide each side by '2'.
x = -1.5y

Simplifying
x = -1.5y
Solution
x = {0.25y, -1.5y}

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