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

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


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

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

Reorder the terms:
((6xy + 4x2) + -1y * (2x + 3y)) = 0
((6xy + 4x2) + -1y * (2x + 3y)) = 0
(6xy + 4x2 + (2x * -1y + 3y * -1y)) = 0
(6xy + 4x2 + (-2xy + -3y2)) = 0

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

Combine like terms: 6xy + -2xy = 4xy
(4xy + 4x2 + -3y2) = 0

Solving
4xy + 4x2 + -3y2 = 0

Solving for variable 'x'.

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

Subproblem 1

Set the factor '(2x + -1y)' equal to zero and attempt to solve: Simplifying 2x + -1y = 0 Solving 2x + -1y = 0 Move all terms containing x to the left, all other terms to the right. Add 'y' to each side of the equation. 2x + -1y + y = 0 + y Combine like terms: -1y + y = 0 2x + 0 = 0 + y 2x = 0 + y Remove the zero: 2x = y Divide each side by '2'. x = 0.5y Simplifying x = 0.5y

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 = {0.5y, -1.5y}

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