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

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