x^2+6y-5z+k=75y-3k+x^3-z

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Solution for x^2+6y-5z+k=75y-3k+x^3-z equation: 


Simplifying
x2 + 6y + -5z + k = 75y + -3k + x3 + -1z

Reorder the terms:
k + x2 + 6y + -5z = 75y + -3k + x3 + -1z

Reorder the terms:
k + x2 + 6y + -5z = -3k + x3 + 75y + -1z

Solving
k + x2 + 6y + -5z = -3k + x3 + 75y + -1z

Solving for variable 'k'.

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

Add '3k' to each side of the equation.
k + x2 + 6y + 3k + -5z = -3k + x3 + 75y + 3k + -1z

Reorder the terms:
k + 3k + x2 + 6y + -5z = -3k + x3 + 75y + 3k + -1z

Combine like terms: k + 3k = 4k
4k + x2 + 6y + -5z = -3k + x3 + 75y + 3k + -1z

Reorder the terms:
4k + x2 + 6y + -5z = -3k + 3k + x3 + 75y + -1z

Combine like terms: -3k + 3k = 0
4k + x2 + 6y + -5z = 0 + x3 + 75y + -1z
4k + x2 + 6y + -5z = x3 + 75y + -1z

Add '-1x2' to each side of the equation.
4k + x2 + 6y + -1x2 + -5z = x3 + 75y + -1x2 + -1z

Reorder the terms:
4k + x2 + -1x2 + 6y + -5z = x3 + 75y + -1x2 + -1z

Combine like terms: x2 + -1x2 = 0
4k + 0 + 6y + -5z = x3 + 75y + -1x2 + -1z
4k + 6y + -5z = x3 + 75y + -1x2 + -1z

Reorder the terms:
4k + 6y + -5z = -1x2 + x3 + 75y + -1z

Add '-6y' to each side of the equation.
4k + 6y + -6y + -5z = -1x2 + x3 + 75y + -6y + -1z

Combine like terms: 6y + -6y = 0
4k + 0 + -5z = -1x2 + x3 + 75y + -6y + -1z
4k + -5z = -1x2 + x3 + 75y + -6y + -1z

Combine like terms: 75y + -6y = 69y
4k + -5z = -1x2 + x3 + 69y + -1z

Add '5z' to each side of the equation.
4k + -5z + 5z = -1x2 + x3 + 69y + -1z + 5z

Combine like terms: -5z + 5z = 0
4k + 0 = -1x2 + x3 + 69y + -1z + 5z
4k = -1x2 + x3 + 69y + -1z + 5z

Combine like terms: -1z + 5z = 4z
4k = -1x2 + x3 + 69y + 4z

Divide each side by '4'.
k = -0.25x2 + 0.25x3 + 17.25y + z

Simplifying
k = -0.25x2 + 0.25x3 + 17.25y + z

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