4k^2+5k=2k^2+k

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Solution for 4k^2+5k=2k^2+k equation:


Simplifying
4k2 + 5k = 2k2 + k

Reorder the terms:
5k + 4k2 = 2k2 + k

Reorder the terms:
5k + 4k2 = k + 2k2

Solving
5k + 4k2 = k + 2k2

Solving for variable 'k'.

Reorder the terms:
5k + -1k + 4k2 + -2k2 = k + 2k2 + -1k + -2k2

Combine like terms: 5k + -1k = 4k
4k + 4k2 + -2k2 = k + 2k2 + -1k + -2k2

Combine like terms: 4k2 + -2k2 = 2k2
4k + 2k2 = k + 2k2 + -1k + -2k2

Reorder the terms:
4k + 2k2 = k + -1k + 2k2 + -2k2

Combine like terms: k + -1k = 0
4k + 2k2 = 0 + 2k2 + -2k2
4k + 2k2 = 2k2 + -2k2

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

Factor out the Greatest Common Factor (GCF), '2k'.
2k(2 + k) = 0

Ignore the factor 2.

Subproblem 1

Set the factor 'k' equal to zero and attempt to solve: Simplifying k = 0 Solving k = 0 Move all terms containing k to the left, all other terms to the right. Simplifying k = 0

Subproblem 2

Set the factor '(2 + k)' equal to zero and attempt to solve: Simplifying 2 + k = 0 Solving 2 + k = 0 Move all terms containing k to the left, all other terms to the right. Add '-2' to each side of the equation. 2 + -2 + k = 0 + -2 Combine like terms: 2 + -2 = 0 0 + k = 0 + -2 k = 0 + -2 Combine like terms: 0 + -2 = -2 k = -2 Simplifying k = -2

Solution

k = {0, -2}

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