4a^2+b^2+c^2-4a+6b-4C+14=0

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Solution for 4a^2+b^2+c^2-4a+6b-4C+14=0 equation:


Simplifying
4a2 + b2 + c2 + -4a + 6b + -4C + 14 = 0

Reorder the terms:
14 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0

Solving
14 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0

Solving for variable 'C'.

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

Add '-14' to each side of the equation.
14 + -4C + -4a + 4a2 + 6b + b2 + -14 + c2 = 0 + -14

Reorder the terms:
14 + -14 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0 + -14

Combine like terms: 14 + -14 = 0
0 + -4C + -4a + 4a2 + 6b + b2 + c2 = 0 + -14
-4C + -4a + 4a2 + 6b + b2 + c2 = 0 + -14

Combine like terms: 0 + -14 = -14
-4C + -4a + 4a2 + 6b + b2 + c2 = -14

Add '4a' to each side of the equation.
-4C + -4a + 4a2 + 6b + b2 + 4a + c2 = -14 + 4a

Reorder the terms:
-4C + -4a + 4a + 4a2 + 6b + b2 + c2 = -14 + 4a

Combine like terms: -4a + 4a = 0
-4C + 0 + 4a2 + 6b + b2 + c2 = -14 + 4a
-4C + 4a2 + 6b + b2 + c2 = -14 + 4a

Add '-4a2' to each side of the equation.
-4C + 4a2 + 6b + b2 + -4a2 + c2 = -14 + 4a + -4a2

Reorder the terms:
-4C + 4a2 + -4a2 + 6b + b2 + c2 = -14 + 4a + -4a2

Combine like terms: 4a2 + -4a2 = 0
-4C + 0 + 6b + b2 + c2 = -14 + 4a + -4a2
-4C + 6b + b2 + c2 = -14 + 4a + -4a2

Add '-6b' to each side of the equation.
-4C + 6b + b2 + -6b + c2 = -14 + 4a + -4a2 + -6b

Reorder the terms:
-4C + 6b + -6b + b2 + c2 = -14 + 4a + -4a2 + -6b

Combine like terms: 6b + -6b = 0
-4C + 0 + b2 + c2 = -14 + 4a + -4a2 + -6b
-4C + b2 + c2 = -14 + 4a + -4a2 + -6b

Add '-1b2' to each side of the equation.
-4C + b2 + -1b2 + c2 = -14 + 4a + -4a2 + -6b + -1b2

Combine like terms: b2 + -1b2 = 0
-4C + 0 + c2 = -14 + 4a + -4a2 + -6b + -1b2
-4C + c2 = -14 + 4a + -4a2 + -6b + -1b2

Add '-1c2' to each side of the equation.
-4C + c2 + -1c2 = -14 + 4a + -4a2 + -6b + -1b2 + -1c2

Combine like terms: c2 + -1c2 = 0
-4C + 0 = -14 + 4a + -4a2 + -6b + -1b2 + -1c2
-4C = -14 + 4a + -4a2 + -6b + -1b2 + -1c2

Divide each side by '-4'.
C = 3.5 + -1a + a2 + 1.5b + 0.25b2 + 0.25c2

Simplifying
C = 3.5 + -1a + a2 + 1.5b + 0.25b2 + 0.25c2

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