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

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


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

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

Reorder the terms:
((4xy + 8x2) + -3y * (2x + y)) = 0
((4xy + 8x2) + -3y * (2x + y)) = 0
(4xy + 8x2 + (2x * -3y + y * -3y)) = 0
(4xy + 8x2 + (-6xy + -3y2)) = 0

Reorder the terms:
(4xy + -6xy + 8x2 + -3y2) = 0

Combine like terms: 4xy + -6xy = -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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