Question

(-4k^4-2k^3-5k^2)+(2k^4-2k^3-3k^2)

Answer 1

Simplifying
5k + 2[-4(k + 3) + -1k] = 4 + -1(2k + 3)

Reorder the terms:
5k + 2[-4(3 + k) + -1k] = 4 + -1(2k + 3)
5k + 2[(3 * -4 + k * -4) + -1k] = 4 + -1(2k + 3)
5k + 2[(-12 + -4k) + -1k] = 4 + -1(2k + 3)

Combine like terms: -4k + -1k = -5k
5k + 2[-12 + -5k] = 4 + -1(2k + 3)
5k + [-12 * 2 + -5k * 2] = 4 + -1(2k + 3)
5k + [-24 + -10k] = 4 + -1(2k + 3)

Reorder the terms:
-24 + 5k + -10k = 4 + -1(2k + 3)

Combine like terms: 5k + -10k = -5k
-24 + -5k = 4 + -1(2k + 3)

Reorder the terms:
-24 + -5k = 4 + -1(3 + 2k)
-24 + -5k = 4 + (3 * -1 + 2k * -1)
-24 + -5k = 4 + (-3 + -2k)

Combine like terms: 4 + -3 = 1
-24 + -5k = 1 + -2k

Solving
-24 + -5k = 1 + -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.
-24 + -5k + 2k = 1 + -2k + 2k

Combine like terms: -5k + 2k = -3k
-24 + -3k = 1 + -2k + 2k

Combine like terms: -2k + 2k = 0
-24 + -3k = 1 + 0
-24 + -3k = 1

Add '24' to each side of the equation.
-24 + 24 + -3k = 1 + 24

Combine like terms: -24 + 24 = 0
0 + -3k = 1 + 24
-3k = 1 + 24

Combine like terms: 1 + 24 = 25
-3k = 25

Divide each side by '-3'.
k = -8.333333333

Simplifying
k = -8.333333333

Answer 2

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