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

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


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

Reorder the terms:
(-18xy + 24x2) + y(4x + -3y) = 0
(-18xy + 24x2) + y(4x + -3y) = 0
-18xy + 24x2 + (4x * y + -3y * y) = 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.
(4x + -3y)(6x + 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 '(6x + y)' equal to zero and attempt to solve:

Simplifying
6x + y = 0

Solving
6x + y = 0

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

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

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

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

Simplifying
x = -0.1666666667y
Solution
x = {0.75y, -0.1666666667y}

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