3(2x+4y-2z)+7(x+y-4z)=0

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Solution for 3(2x+4y-2z)+7(x+y-4z)=0 equation:


Simplifying
3(2x + 4y + -2z) + 7(x + y + -4z) = 0
(2x * 3 + 4y * 3 + -2z * 3) + 7(x + y + -4z) = 0
(6x + 12y + -6z) + 7(x + y + -4z) = 0
6x + 12y + -6z + (x * 7 + y * 7 + -4z * 7) = 0
6x + 12y + -6z + (7x + 7y + -28z) = 0

Reorder the terms:
6x + 7x + 12y + 7y + -6z + -28z = 0

Combine like terms: 6x + 7x = 13x
13x + 12y + 7y + -6z + -28z = 0

Combine like terms: 12y + 7y = 19y
13x + 19y + -6z + -28z = 0

Combine like terms: -6z + -28z = -34z
13x + 19y + -34z = 0

Solving
13x + 19y + -34z = 0

Solving for variable 'x'.

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

Add '-19y' to each side of the equation.
13x + 19y + -19y + -34z = 0 + -19y

Combine like terms: 19y + -19y = 0
13x + 0 + -34z = 0 + -19y
13x + -34z = 0 + -19y
Remove the zero:
13x + -34z = -19y

Add '34z' to each side of the equation.
13x + -34z + 34z = -19y + 34z

Combine like terms: -34z + 34z = 0
13x + 0 = -19y + 34z
13x = -19y + 34z

Divide each side by '13'.
x = -1.461538462y + 2.615384615z

Simplifying
x = -1.461538462y + 2.615384615z

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