k^2-4k-7=2k

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Solution for k^2-4k-7=2k equation:


Simplifying
k2 + -4k + -7 = 2k

Reorder the terms:
-7 + -4k + k2 = 2k

Solving
-7 + -4k + k2 = 2k

Solving for variable 'k'.

Reorder the terms:
-7 + -4k + -2k + k2 = 2k + -2k

Combine like terms: -4k + -2k = -6k
-7 + -6k + k2 = 2k + -2k

Combine like terms: 2k + -2k = 0
-7 + -6k + k2 = 0

Factor a trinomial.
(-1 + -1k)(7 + -1k) = 0

Subproblem 1

Set the factor '(-1 + -1k)' equal to zero and attempt to solve: Simplifying -1 + -1k = 0 Solving -1 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '1' to each side of the equation. -1 + 1 + -1k = 0 + 1 Combine like terms: -1 + 1 = 0 0 + -1k = 0 + 1 -1k = 0 + 1 Combine like terms: 0 + 1 = 1 -1k = 1 Divide each side by '-1'. k = -1 Simplifying k = -1

Subproblem 2

Set the factor '(7 + -1k)' equal to zero and attempt to solve: Simplifying 7 + -1k = 0 Solving 7 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-7' to each side of the equation. 7 + -7 + -1k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -1k = 0 + -7 -1k = 0 + -7 Combine like terms: 0 + -7 = -7 -1k = -7 Divide each side by '-1'. k = 7 Simplifying k = 7

Solution

k = {-1, 7}

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