2z(x^2+3xy-4y^2)-2z(x+y)(x-y)=

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Solution for 2z(x^2+3xy-4y^2)-2z(x+y)(x-y)= equation: 


Simplifying
2z(x2 + 3xy + -4y2) + -2z(x + y)(x + -1y) = 0

Reorder the terms:
2z(3xy + x2 + -4y2) + -2z(x + y)(x + -1y) = 0
(3xy * 2z + x2 * 2z + -4y2 * 2z) + -2z(x + y)(x + -1y) = 0
(6xyz + 2x2z + -8y2z) + -2z(x + y)(x + -1y) = 0

Multiply (x + y) * (x + -1y)
6xyz + 2x2z + -8y2z + -2z(x(x + -1y) + y(x + -1y)) = 0
6xyz + 2x2z + -8y2z + -2z((x * x + -1y * x) + y(x + -1y)) = 0

Reorder the terms:
6xyz + 2x2z + -8y2z + -2z((-1xy + x2) + y(x + -1y)) = 0
6xyz + 2x2z + -8y2z + -2z((-1xy + x2) + y(x + -1y)) = 0
6xyz + 2x2z + -8y2z + -2z(-1xy + x2 + (x * y + -1y * y)) = 0
6xyz + 2x2z + -8y2z + -2z(-1xy + x2 + (xy + -1y2)) = 0

Reorder the terms:
6xyz + 2x2z + -8y2z + -2z(-1xy + xy + x2 + -1y2) = 0

Combine like terms: -1xy + xy = 0
6xyz + 2x2z + -8y2z + -2z(0 + x2 + -1y2) = 0
6xyz + 2x2z + -8y2z + -2z(x2 + -1y2) = 0
6xyz + 2x2z + -8y2z + (x2 * -2z + -1y2 * -2z) = 0
6xyz + 2x2z + -8y2z + (-2x2z + 2y2z) = 0

Reorder the terms:
6xyz + 2x2z + -2x2z + -8y2z + 2y2z = 0

Combine like terms: 2x2z + -2x2z = 0
6xyz + 0 + -8y2z + 2y2z = 0
6xyz + -8y2z + 2y2z = 0

Combine like terms: -8y2z + 2y2z = -6y2z
6xyz + -6y2z = 0

Solving
6xyz + -6y2z = 0

Solving for variable 'x'.

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

Add '6y2z' to each side of the equation.
6xyz + -6y2z + 6y2z = 0 + 6y2z

Combine like terms: -6y2z + 6y2z = 0
6xyz + 0 = 0 + 6y2z
6xyz = 0 + 6y2z
Remove the zero:
6xyz = 6y2z

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

Simplifying
x = y

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