0=-3k^2+k+14

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Solution for 0=-3k^2+k+14 equation:


Simplifying
0 = -3k2 + k + 14

Reorder the terms:
0 = 14 + k + -3k2

Solving
0 = 14 + k + -3k2

Solving for variable 'k'.

Combine like terms: 0 + -14 = -14
-14 + -1k + 3k2 = 14 + k + -3k2 + -14 + -1k + 3k2

Reorder the terms:
-14 + -1k + 3k2 = 14 + -14 + k + -1k + -3k2 + 3k2

Combine like terms: 14 + -14 = 0
-14 + -1k + 3k2 = 0 + k + -1k + -3k2 + 3k2
-14 + -1k + 3k2 = k + -1k + -3k2 + 3k2

Combine like terms: k + -1k = 0
-14 + -1k + 3k2 = 0 + -3k2 + 3k2
-14 + -1k + 3k2 = -3k2 + 3k2

Combine like terms: -3k2 + 3k2 = 0
-14 + -1k + 3k2 = 0

Factor a trinomial.
(-2 + -1k)(7 + -3k) = 0

Subproblem 1

Set the factor '(-2 + -1k)' equal to zero and attempt to solve: Simplifying -2 + -1k = 0 Solving -2 + -1k = 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 + -1k = 0 + 2 Combine like terms: -2 + 2 = 0 0 + -1k = 0 + 2 -1k = 0 + 2 Combine like terms: 0 + 2 = 2 -1k = 2 Divide each side by '-1'. k = -2 Simplifying k = -2

Subproblem 2

Set the factor '(7 + -3k)' equal to zero and attempt to solve: Simplifying 7 + -3k = 0 Solving 7 + -3k = 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 + -3k = 0 + -7 Combine like terms: 7 + -7 = 0 0 + -3k = 0 + -7 -3k = 0 + -7 Combine like terms: 0 + -7 = -7 -3k = -7 Divide each side by '-3'. k = 2.333333333 Simplifying k = 2.333333333

Solution

k = {-2, 2.333333333}

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