2(2k+1)x+5(2k+1)y-3k-1=0

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Solution for 2(2k+1)x+5(2k+1)y-3k-1=0 equation: 


Simplifying
2(2k + 1) * x + 5(2k + 1) * y + -3k + -1 = 0

Reorder the terms:
2(1 + 2k) * x + 5(2k + 1) * y + -3k + -1 = 0

Reorder the terms for easier multiplication:
2x(1 + 2k) + 5(2k + 1) * y + -3k + -1 = 0
(1 * 2x + 2k * 2x) + 5(2k + 1) * y + -3k + -1 = 0

Reorder the terms:
(4kx + 2x) + 5(2k + 1) * y + -3k + -1 = 0
(4kx + 2x) + 5(2k + 1) * y + -3k + -1 = 0

Reorder the terms:
4kx + 2x + 5(1 + 2k) * y + -3k + -1 = 0

Reorder the terms for easier multiplication:
4kx + 2x + 5y(1 + 2k) + -3k + -1 = 0
4kx + 2x + (1 * 5y + 2k * 5y) + -3k + -1 = 0

Reorder the terms:
4kx + 2x + (10ky + 5y) + -3k + -1 = 0
4kx + 2x + (10ky + 5y) + -3k + -1 = 0

Reorder the terms:
-1 + -3k + 4kx + 10ky + 2x + 5y = 0

Solving
-1 + -3k + 4kx + 10ky + 2x + 5y = 0

Solving for variable 'k'.

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

Add '1' to each side of the equation.
-1 + -3k + 4kx + 10ky + 2x + 1 + 5y = 0 + 1

Reorder the terms:
-1 + 1 + -3k + 4kx + 10ky + 2x + 5y = 0 + 1

Combine like terms: -1 + 1 = 0
0 + -3k + 4kx + 10ky + 2x + 5y = 0 + 1
-3k + 4kx + 10ky + 2x + 5y = 0 + 1

Combine like terms: 0 + 1 = 1
-3k + 4kx + 10ky + 2x + 5y = 1

Add '-2x' to each side of the equation.
-3k + 4kx + 10ky + 2x + -2x + 5y = 1 + -2x

Combine like terms: 2x + -2x = 0
-3k + 4kx + 10ky + 0 + 5y = 1 + -2x
-3k + 4kx + 10ky + 5y = 1 + -2x

Add '-5y' to each side of the equation.
-3k + 4kx + 10ky + 5y + -5y = 1 + -2x + -5y

Combine like terms: 5y + -5y = 0
-3k + 4kx + 10ky + 0 = 1 + -2x + -5y
-3k + 4kx + 10ky = 1 + -2x + -5y

Reorder the terms:
-1 + -3k + 4kx + 10ky + 2x + 5y = 1 + -2x + -5y + -1 + 2x + 5y

Reorder the terms:
-1 + -3k + 4kx + 10ky + 2x + 5y = 1 + -1 + -2x + 2x + -5y + 5y

Combine like terms: 1 + -1 = 0
-1 + -3k + 4kx + 10ky + 2x + 5y = 0 + -2x + 2x + -5y + 5y
-1 + -3k + 4kx + 10ky + 2x + 5y = -2x + 2x + -5y + 5y

Combine like terms: -2x + 2x = 0
-1 + -3k + 4kx + 10ky + 2x + 5y = 0 + -5y + 5y
-1 + -3k + 4kx + 10ky + 2x + 5y = -5y + 5y

Combine like terms: -5y + 5y = 0
-1 + -3k + 4kx + 10ky + 2x + 5y = 0

The solution to this equation could not be determined.

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