x^2+8(2K-1)x+12(3K+1)=0

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Solution for x^2+8(2K-1)x+12(3K+1)=0 equation:


Simplifying
x2 + 8(2K + -1) * x + 12(3K + 1) = 0

Reorder the terms:
x2 + 8(-1 + 2K) * x + 12(3K + 1) = 0

Reorder the terms for easier multiplication:
x2 + 8x(-1 + 2K) + 12(3K + 1) = 0
x2 + (-1 * 8x + 2K * 8x) + 12(3K + 1) = 0
x2 + (-8x + 16xK) + 12(3K + 1) = 0

Reorder the terms:
x2 + -8x + 16xK + 12(1 + 3K) = 0
x2 + -8x + 16xK + (1 * 12 + 3K * 12) = 0
x2 + -8x + 16xK + (12 + 36K) = 0

Reorder the terms:
12 + 36K + -8x + 16xK + x2 = 0

Solving
12 + 36K + -8x + 16xK + x2 = 0

Solving for variable 'K'.

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

Add '-12' to each side of the equation.
12 + 36K + -8x + 16xK + -12 + x2 = 0 + -12

Reorder the terms:
12 + -12 + 36K + -8x + 16xK + x2 = 0 + -12

Combine like terms: 12 + -12 = 0
0 + 36K + -8x + 16xK + x2 = 0 + -12
36K + -8x + 16xK + x2 = 0 + -12

Combine like terms: 0 + -12 = -12
36K + -8x + 16xK + x2 = -12

Add '8x' to each side of the equation.
36K + -8x + 16xK + 8x + x2 = -12 + 8x

Reorder the terms:
36K + -8x + 8x + 16xK + x2 = -12 + 8x

Combine like terms: -8x + 8x = 0
36K + 0 + 16xK + x2 = -12 + 8x
36K + 16xK + x2 = -12 + 8x

Add '-1x2' to each side of the equation.
36K + 16xK + x2 + -1x2 = -12 + 8x + -1x2

Combine like terms: x2 + -1x2 = 0
36K + 16xK + 0 = -12 + 8x + -1x2
36K + 16xK = -12 + 8x + -1x2

Reorder the terms:
12 + 36K + -8x + 16xK + x2 = -12 + 8x + -1x2 + 12 + -8x + x2

Reorder the terms:
12 + 36K + -8x + 16xK + x2 = -12 + 12 + 8x + -8x + -1x2 + x2

Combine like terms: -12 + 12 = 0
12 + 36K + -8x + 16xK + x2 = 0 + 8x + -8x + -1x2 + x2
12 + 36K + -8x + 16xK + x2 = 8x + -8x + -1x2 + x2

Combine like terms: 8x + -8x = 0
12 + 36K + -8x + 16xK + x2 = 0 + -1x2 + x2
12 + 36K + -8x + 16xK + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
12 + 36K + -8x + 16xK + x2 = 0

The solution to this equation could not be determined.

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