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

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


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

Reorder the terms:
(6x + y)(7y + -4x) = 0

Reorder the terms:
(6x + y)(-4x + 7y) = 0

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

Reorder the terms:
((42xy + -24x2) + y(-4x + 7y)) = 0
((42xy + -24x2) + y(-4x + 7y)) = 0
(42xy + -24x2 + (-4x * y + 7y * y)) = 0
(42xy + -24x2 + (-4xy + 7y2)) = 0

Reorder the terms:
(42xy + -4xy + -24x2 + 7y2) = 0

Combine like terms: 42xy + -4xy = 38xy
(38xy + -24x2 + 7y2) = 0

Solving
38xy + -24x2 + 7y2 = 0

Solving for variable 'x'.

Factor a trinomial.
(-6x + -1y)(4x + -7y) = 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 + -7y)' equal to zero and attempt to solve:

Simplifying
4x + -7y = 0

Solving
4x + -7y = 0

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

Add '7y' to each side of the equation.
4x + -7y + 7y = 0 + 7y

Combine like terms: -7y + 7y = 0
4x + 0 = 0 + 7y
4x = 0 + 7y
Remove the zero:
4x = 7y

Divide each side by '4'.
x = 1.75y

Simplifying
x = 1.75y
Solution
x = {-0.1666666667y, 1.75y}

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