0.5k(3k-1)+(3k-1)=0.5(k+1)3k

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Solution for 0.5k(3k-1)+(3k-1)=0.5(k+1)3k equation: 


Simplifying
0.5k(3k + -1) + (3k + -1) = 0.5(k + 1) * 3k

Reorder the terms:
0.5k(-1 + 3k) + (3k + -1) = 0.5(k + 1) * 3k
(-1 * 0.5k + 3k * 0.5k) + (3k + -1) = 0.5(k + 1) * 3k
(-0.5k + 1.5k2) + (3k + -1) = 0.5(k + 1) * 3k

Reorder the terms:
-0.5k + 1.5k2 + (-1 + 3k) = 0.5(k + 1) * 3k

Remove parenthesis around (-1 + 3k)
-0.5k + 1.5k2 + -1 + 3k = 0.5(k + 1) * 3k

Reorder the terms:
-1 + -0.5k + 3k + 1.5k2 = 0.5(k + 1) * 3k

Combine like terms: -0.5k + 3k = 2.5k
-1 + 2.5k + 1.5k2 = 0.5(k + 1) * 3k

Reorder the terms:
-1 + 2.5k + 1.5k2 = 0.5(1 + k) * 3k

Reorder the terms for easier multiplication:
-1 + 2.5k + 1.5k2 = 0.5 * 3k(1 + k)

Multiply 0.5 * 3
-1 + 2.5k + 1.5k2 = 1.5k(1 + k)
-1 + 2.5k + 1.5k2 = (1 * 1.5k + k * 1.5k)
-1 + 2.5k + 1.5k2 = (1.5k + 1.5k2)

Add '-1.5k2' to each side of the equation.
-1 + 2.5k + 1.5k2 + -1.5k2 = 1.5k + 1.5k2 + -1.5k2

Combine like terms: 1.5k2 + -1.5k2 = 0.0
-1 + 2.5k + 0.0 = 1.5k + 1.5k2 + -1.5k2
-1 + 2.5k = 1.5k + 1.5k2 + -1.5k2

Combine like terms: 1.5k2 + -1.5k2 = 0.0
-1 + 2.5k = 1.5k + 0.0
-1 + 2.5k = 1.5k

Solving
-1 + 2.5k = 1.5k

Solving for variable 'k'.

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

Add '-1.5k' to each side of the equation.
-1 + 2.5k + -1.5k = 1.5k + -1.5k

Combine like terms: 2.5k + -1.5k = 1k
-1 + 1k = 1.5k + -1.5k

Combine like terms: 1.5k + -1.5k = 0.0
-1 + 1k = 0.0

Add '1' to each side of the equation.
-1 + 1 + 1k = 0.0 + 1

Combine like terms: -1 + 1 = 0
0 + 1k = 0.0 + 1
1k = 0.0 + 1

Combine like terms: 0.0 + 1 = 1
1k = 1

Divide each side by '1'.
k = 1

Simplifying
k = 1

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