2k(-3k+4)+6(k^2+10)=k(4k+8)-2k(2k+5)

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Solution for 2k(-3k+4)+6(k^2+10)=k(4k+8)-2k(2k+5) equation: 


Simplifying
2k(-3k + 4) + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
2k(4 + -3k) + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)
(4 * 2k + -3k * 2k) + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)
(8k + -6k2) + 6(k2 + 10) = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
8k + -6k2 + 6(10 + k2) = k(4k + 8) + -2k(2k + 5)
8k + -6k2 + (10 * 6 + k2 * 6) = k(4k + 8) + -2k(2k + 5)
8k + -6k2 + (60 + 6k2) = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
60 + 8k + -6k2 + 6k2 = k(4k + 8) + -2k(2k + 5)

Combine like terms: -6k2 + 6k2 = 0
60 + 8k + 0 = k(4k + 8) + -2k(2k + 5)
60 + 8k = k(4k + 8) + -2k(2k + 5)

Reorder the terms:
60 + 8k = k(8 + 4k) + -2k(2k + 5)
60 + 8k = (8 * k + 4k * k) + -2k(2k + 5)
60 + 8k = (8k + 4k2) + -2k(2k + 5)

Reorder the terms:
60 + 8k = 8k + 4k2 + -2k(5 + 2k)
60 + 8k = 8k + 4k2 + (5 * -2k + 2k * -2k)
60 + 8k = 8k + 4k2 + (-10k + -4k2)

Reorder the terms:
60 + 8k = 8k + -10k + 4k2 + -4k2

Combine like terms: 8k + -10k = -2k
60 + 8k = -2k + 4k2 + -4k2

Combine like terms: 4k2 + -4k2 = 0
60 + 8k = -2k + 0
60 + 8k = -2k

Solving
60 + 8k = -2k

Solving for variable 'k'.

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

Add '2k' to each side of the equation.
60 + 8k + 2k = -2k + 2k

Combine like terms: 8k + 2k = 10k
60 + 10k = -2k + 2k

Combine like terms: -2k + 2k = 0
60 + 10k = 0

Add '-60' to each side of the equation.
60 + -60 + 10k = 0 + -60

Combine like terms: 60 + -60 = 0
0 + 10k = 0 + -60
10k = 0 + -60

Combine like terms: 0 + -60 = -60
10k = -60

Divide each side by '10'.
k = -6

Simplifying
k = -6

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