[7x-(4y+x)][7x+(4y+x)]=

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

Simplifying
[7x + -1(4y + x)][7x + (4y + x)] = 0

Reorder the terms:
[7x + -1(x + 4y)][7x + (4y + x)] = 0
[7x + (x * -1 + 4y * -1)][7x + (4y + x)] = 0
[7x + (-1x + -4y)][7x + (4y + x)] = 0

Combine like terms: 7x + -1x = 6x
[6x + -4y][7x + (4y + x)] = 0

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

Remove parenthesis around (x + 4y)
[6x + -4y][7x + x + 4y] = 0

Combine like terms: 7x + x = 8x
[6x + -4y][8x + 4y] = 0

Multiply [6x + -4y] * [8x + 4y]
[6x * [8x + 4y] + -4y * [8x + 4y]] = 0
[[8x * 6x + 4y * 6x] + -4y * [8x + 4y]] = 0

Reorder the terms:
[[24xy + 48x2] + -4y * [8x + 4y]] = 0
[[24xy + 48x2] + -4y * [8x + 4y]] = 0
[24xy + 48x2 + [8x * -4y + 4y * -4y]] = 0
[24xy + 48x2 + [-32xy + -16y2]] = 0

Reorder the terms:
[24xy + -32xy + 48x2 + -16y2] = 0

Combine like terms: 24xy + -32xy = -8xy
[-8xy + 48x2 + -16y2] = 0

Solving
-8xy + 48x2 + -16y2 = 0

Solving for variable 'x'.

Factor out the Greatest Common Factor (GCF), '8'.
8(-1xy + 6x2 + -2y2) = 0

Factor a trinomial.
8((3x + -2y)(2x + y)) = 0

Ignore the factor 8.
Subproblem 1
Set the factor '(3x + -2y)' equal to zero and attempt to solve:

Simplifying
3x + -2y = 0

Solving
3x + -2y = 0

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

Add '2y' to each side of the equation.
3x + -2y + 2y = 0 + 2y

Combine like terms: -2y + 2y = 0
3x + 0 = 0 + 2y
3x = 0 + 2y
Remove the zero:
3x = 2y

Divide each side by '3'.
x = 0.6666666667y

Simplifying
x = 0.6666666667y
Subproblem 2
Set the factor '(2x + y)' equal to zero and attempt to solve:

Simplifying
2x + y = 0

Solving
2x + y = 0

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

Add '-1y' to each side of the equation.
2x + y + -1y = 0 + -1y

Combine like terms: y + -1y = 0
2x + 0 = 0 + -1y
2x = 0 + -1y
Remove the zero:
2x = -1y

Divide each side by '2'.
x = -0.5y

Simplifying
x = -0.5y
Solution
x = {0.6666666667y, -0.5y}