3(x-y+z)(x+y-z)=

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


Simplifying
3(x + -1y + z)(x + y + -1z) = 0

Multiply (x + -1y + z) * (x + y + -1z)
3(x(x + y + -1z) + -1y * (x + y + -1z) + z(x + y + -1z)) = 0
3((x * x + y * x + -1z * x) + -1y * (x + y + -1z) + z(x + y + -1z)) = 0

Reorder the terms:
3((xy + -1xz + x2) + -1y * (x + y + -1z) + z(x + y + -1z)) = 0
3((xy + -1xz + x2) + -1y * (x + y + -1z) + z(x + y + -1z)) = 0
3(xy + -1xz + x2 + (x * -1y + y * -1y + -1z * -1y) + z(x + y + -1z)) = 0

Reorder the terms:
3(xy + -1xz + x2 + (-1xy + 1yz + -1y2) + z(x + y + -1z)) = 0
3(xy + -1xz + x2 + (-1xy + 1yz + -1y2) + z(x + y + -1z)) = 0
3(xy + -1xz + x2 + -1xy + 1yz + -1y2 + (x * z + y * z + -1z * z)) = 0
3(xy + -1xz + x2 + -1xy + 1yz + -1y2 + (xz + yz + -1z2)) = 0

Reorder the terms:
3(xy + -1xy + -1xz + xz + x2 + 1yz + yz + -1y2 + -1z2) = 0

Combine like terms: xy + -1xy = 0
3(0 + -1xz + xz + x2 + 1yz + yz + -1y2 + -1z2) = 0
3(-1xz + xz + x2 + 1yz + yz + -1y2 + -1z2) = 0

Combine like terms: -1xz + xz = 0
3(0 + x2 + 1yz + yz + -1y2 + -1z2) = 0
3(x2 + 1yz + yz + -1y2 + -1z2) = 0

Combine like terms: 1yz + yz = 2yz
3(x2 + 2yz + -1y2 + -1z2) = 0
(x2 * 3 + 2yz * 3 + -1y2 * 3 + -1z2 * 3) = 0
(3x2 + 6yz + -3y2 + -3z2) = 0

Solving
3x2 + 6yz + -3y2 + -3z2 = 0

Solving for variable 'x'.

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

Add '-6yz' to each side of the equation.
3x2 + 6yz + -3y2 + -6yz + -3z2 = 0 + -6yz

Reorder the terms:
3x2 + 6yz + -6yz + -3y2 + -3z2 = 0 + -6yz

Combine like terms: 6yz + -6yz = 0
3x2 + 0 + -3y2 + -3z2 = 0 + -6yz
3x2 + -3y2 + -3z2 = 0 + -6yz
Remove the zero:
3x2 + -3y2 + -3z2 = -6yz

Add '3y2' to each side of the equation.
3x2 + -3y2 + 3y2 + -3z2 = -6yz + 3y2

Combine like terms: -3y2 + 3y2 = 0
3x2 + 0 + -3z2 = -6yz + 3y2
3x2 + -3z2 = -6yz + 3y2

Add '3z2' to each side of the equation.
3x2 + -3z2 + 3z2 = -6yz + 3y2 + 3z2

Combine like terms: -3z2 + 3z2 = 0
3x2 + 0 = -6yz + 3y2 + 3z2
3x2 = -6yz + 3y2 + 3z2

Divide each side by '3'.
x2 = -2yz + y2 + z2

Simplifying
x2 = -2yz + y2 + z2

Reorder the terms:
x2 + 2yz + -1y2 + -1z2 = -2yz + 2yz + y2 + -1y2 + z2 + -1z2

Combine like terms: -2yz + 2yz = 0
x2 + 2yz + -1y2 + -1z2 = 0 + y2 + -1y2 + z2 + -1z2
x2 + 2yz + -1y2 + -1z2 = y2 + -1y2 + z2 + -1z2

Combine like terms: y2 + -1y2 = 0
x2 + 2yz + -1y2 + -1z2 = 0 + z2 + -1z2
x2 + 2yz + -1y2 + -1z2 = z2 + -1z2

Combine like terms: z2 + -1z2 = 0
x2 + 2yz + -1y2 + -1z2 = 0

The solution to this equation could not be determined.

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