(4x+y)(6x-7y)=

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Solution for (4x+y)(6x-7y)= equation: 


Simplifying
(4x + y)(6x + -7y) = 0

Multiply (4x + y) * (6x + -7y)
(4x * (6x + -7y) + y(6x + -7y)) = 0
((6x * 4x + -7y * 4x) + y(6x + -7y)) = 0

Reorder the terms:
((-28xy + 24x2) + y(6x + -7y)) = 0
((-28xy + 24x2) + y(6x + -7y)) = 0
(-28xy + 24x2 + (6x * y + -7y * y)) = 0
(-28xy + 24x2 + (6xy + -7y2)) = 0

Reorder the terms:
(-28xy + 6xy + 24x2 + -7y2) = 0

Combine like terms: -28xy + 6xy = -22xy
(-22xy + 24x2 + -7y2) = 0

Solving
-22xy + 24x2 + -7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(6x + -7y)(4x + y) = 0


Subproblem 1
Set the factor '(6x + -7y)' equal to zero and attempt to solve:

Simplifying
6x + -7y = 0

Solving
6x + -7y = 0

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

Add '7y' to each side of the equation.
6x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
6x + 0 = 0 + 7y
6x = 0 + 7y
Remove the zero:
6x = 7y

Divide each side by '6'.
x = 1.166666667y

Simplifying
x = 1.166666667y

Subproblem 2
Set the factor '(4x + y)' equal to zero and attempt to solve:

Simplifying
4x + y = 0

Solving
4x + y = 0

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

Add '-1y' to each side of the equation.
4x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
4x + 0 = 0 + -1y
4x = 0 + -1y
Remove the zero:
4x = -1y

Divide each side by '4'.
x = -0.25y

Simplifying
x = -0.25y
Solution
x = {1.166666667y, -0.25y}

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