k(3k-1)+2(k+1)=(k+1)(3(k+1)-1)

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Solution for k(3k-1)+2(k+1)=(k+1)(3(k+1)-1) equation: 


Simplifying
k(3k + -1) + 2(k + 1) = (k + 1)(3(k + 1) + -1)

Reorder the terms:
k(-1 + 3k) + 2(k + 1) = (k + 1)(3(k + 1) + -1)
(-1 * k + 3k * k) + 2(k + 1) = (k + 1)(3(k + 1) + -1)
(-1k + 3k2) + 2(k + 1) = (k + 1)(3(k + 1) + -1)

Reorder the terms:
-1k + 3k2 + 2(1 + k) = (k + 1)(3(k + 1) + -1)
-1k + 3k2 + (1 * 2 + k * 2) = (k + 1)(3(k + 1) + -1)
-1k + 3k2 + (2 + 2k) = (k + 1)(3(k + 1) + -1)

Reorder the terms:
2 + -1k + 2k + 3k2 = (k + 1)(3(k + 1) + -1)

Combine like terms: -1k + 2k = 1k
2 + 1k + 3k2 = (k + 1)(3(k + 1) + -1)

Reorder the terms:
2 + 1k + 3k2 = (1 + k)(3(k + 1) + -1)

Reorder the terms:
2 + 1k + 3k2 = (1 + k)(3(1 + k) + -1)
2 + 1k + 3k2 = (1 + k)((1 * 3 + k * 3) + -1)
2 + 1k + 3k2 = (1 + k)((3 + 3k) + -1)

Reorder the terms:
2 + 1k + 3k2 = (1 + k)(3 + -1 + 3k)

Combine like terms: 3 + -1 = 2
2 + 1k + 3k2 = (1 + k)(2 + 3k)

Multiply (1 + k) * (2 + 3k)
2 + 1k + 3k2 = (1(2 + 3k) + k(2 + 3k))
2 + 1k + 3k2 = ((2 * 1 + 3k * 1) + k(2 + 3k))
2 + 1k + 3k2 = ((2 + 3k) + k(2 + 3k))
2 + 1k + 3k2 = (2 + 3k + (2 * k + 3k * k))
2 + 1k + 3k2 = (2 + 3k + (2k + 3k2))

Combine like terms: 3k + 2k = 5k
2 + 1k + 3k2 = (2 + 5k + 3k2)

Add '-2' to each side of the equation.
2 + 1k + -2 + 3k2 = 2 + 5k + -2 + 3k2

Reorder the terms:
2 + -2 + 1k + 3k2 = 2 + 5k + -2 + 3k2

Combine like terms: 2 + -2 = 0
0 + 1k + 3k2 = 2 + 5k + -2 + 3k2
1k + 3k2 = 2 + 5k + -2 + 3k2

Reorder the terms:
1k + 3k2 = 2 + -2 + 5k + 3k2

Combine like terms: 2 + -2 = 0
1k + 3k2 = 0 + 5k + 3k2
1k + 3k2 = 5k + 3k2

Add '-3k2' to each side of the equation.
1k + 3k2 + -3k2 = 5k + 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
1k + 0 = 5k + 3k2 + -3k2
1k = 5k + 3k2 + -3k2

Combine like terms: 3k2 + -3k2 = 0
1k = 5k + 0
1k = 5k

Solving
1k = 5k

Solving for variable 'k'.

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

Add '-5k' to each side of the equation.
1k + -5k = 5k + -5k

Combine like terms: 1k + -5k = -4k
-4k = 5k + -5k

Combine like terms: 5k + -5k = 0
-4k = 0

Divide each side by '-4'.
k = 0

Simplifying
k = 0

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