(1+2k)x^2-10x+(k-2)=0

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Solution for (1+2k)x^2-10x+(k-2)=0 equation: 


Simplifying
(1 + 2k) * x2 + -10x + (k + -2) = 0

Reorder the terms for easier multiplication:
x2(1 + 2k) + -10x + (k + -2) = 0
(1 * x2 + 2k * x2) + -10x + (k + -2) = 0

Reorder the terms:
(2kx2 + 1x2) + -10x + (k + -2) = 0
(2kx2 + 1x2) + -10x + (k + -2) = 0

Reorder the terms:
2kx2 + 1x2 + -10x + (-2 + k) = 0

Remove parenthesis around (-2 + k)
2kx2 + 1x2 + -10x + -2 + k = 0

Reorder the terms:
-2 + k + 2kx2 + -10x + 1x2 = 0

Solving
-2 + k + 2kx2 + -10x + 1x2 = 0

Solving for variable 'k'.

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

Add '2' to each side of the equation.
-2 + k + 2kx2 + -10x + 2 + 1x2 = 0 + 2

Reorder the terms:
-2 + 2 + k + 2kx2 + -10x + 1x2 = 0 + 2

Combine like terms: -2 + 2 = 0
0 + k + 2kx2 + -10x + 1x2 = 0 + 2
k + 2kx2 + -10x + 1x2 = 0 + 2

Combine like terms: 0 + 2 = 2
k + 2kx2 + -10x + 1x2 = 2

Add '10x' to each side of the equation.
k + 2kx2 + -10x + 10x + 1x2 = 2 + 10x

Combine like terms: -10x + 10x = 0
k + 2kx2 + 0 + 1x2 = 2 + 10x
k + 2kx2 + 1x2 = 2 + 10x

Add '-1x2' to each side of the equation.
k + 2kx2 + 1x2 + -1x2 = 2 + 10x + -1x2

Combine like terms: 1x2 + -1x2 = 0
k + 2kx2 + 0 = 2 + 10x + -1x2
k + 2kx2 = 2 + 10x + -1x2

Reorder the terms:
-2 + k + 2kx2 + -10x + x2 = 2 + 10x + -1x2 + -2 + -10x + x2

Reorder the terms:
-2 + k + 2kx2 + -10x + x2 = 2 + -2 + 10x + -10x + -1x2 + x2

Combine like terms: 2 + -2 = 0
-2 + k + 2kx2 + -10x + x2 = 0 + 10x + -10x + -1x2 + x2
-2 + k + 2kx2 + -10x + x2 = 10x + -10x + -1x2 + x2

Combine like terms: 10x + -10x = 0
-2 + k + 2kx2 + -10x + x2 = 0 + -1x2 + x2
-2 + k + 2kx2 + -10x + x2 = -1x2 + x2

Combine like terms: -1x2 + x2 = 0
-2 + k + 2kx2 + -10x + x2 = 0

The solution to this equation could not be determined.

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