(6x-y)(4x+3y)=0

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Solution for (6x-y)(4x+3y)=0 equation: 


Simplifying
(6x + -1y)(4x + 3y) = 0

Multiply (6x + -1y) * (4x + 3y)
(6x * (4x + 3y) + -1y * (4x + 3y)) = 0
((4x * 6x + 3y * 6x) + -1y * (4x + 3y)) = 0

Reorder the terms:
((18xy + 24x2) + -1y * (4x + 3y)) = 0
((18xy + 24x2) + -1y * (4x + 3y)) = 0
(18xy + 24x2 + (4x * -1y + 3y * -1y)) = 0
(18xy + 24x2 + (-4xy + -3y2)) = 0

Reorder the terms:
(18xy + -4xy + 24x2 + -3y2) = 0

Combine like terms: 18xy + -4xy = 14xy
(14xy + 24x2 + -3y2) = 0

Solving
14xy + 24x2 + -3y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + -1y)(4x + 3y) = 0


Subproblem 1
Set the factor '(6x + -1y)' equal to zero and attempt to solve:

Simplifying
6x + -1y = 0

Solving
6x + -1y = 0

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

Add 'y' to each side of the equation.
6x + -1y + y = 0 + y

Combine like terms: -1y + y = 0
6x + 0 = 0 + y
6x = 0 + y
Remove the zero:
6x = y

Divide each side by '6'.
x = 0.1666666667y

Simplifying
x = 0.1666666667y

Subproblem 2
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
Solution
x = {0.1666666667y, -0.75y}

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