3k^2=3k+60

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Solution for 3k^2=3k+60 equation:


Simplifying
3k2 = 3k + 60

Reorder the terms:
3k2 = 60 + 3k

Solving
3k2 = 60 + 3k

Solving for variable 'k'.

Reorder the terms:
-60 + -3k + 3k2 = 60 + 3k + -60 + -3k

Reorder the terms:
-60 + -3k + 3k2 = 60 + -60 + 3k + -3k

Combine like terms: 60 + -60 = 0
-60 + -3k + 3k2 = 0 + 3k + -3k
-60 + -3k + 3k2 = 3k + -3k

Combine like terms: 3k + -3k = 0
-60 + -3k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-20 + -1k + k2) = 0

Factor a trinomial.
3((-4 + -1k)(5 + -1k)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-4 + -1k)' equal to zero and attempt to solve: Simplifying -4 + -1k = 0 Solving -4 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '4' to each side of the equation. -4 + 4 + -1k = 0 + 4 Combine like terms: -4 + 4 = 0 0 + -1k = 0 + 4 -1k = 0 + 4 Combine like terms: 0 + 4 = 4 -1k = 4 Divide each side by '-1'. k = -4 Simplifying k = -4

Subproblem 2

Set the factor '(5 + -1k)' equal to zero and attempt to solve: Simplifying 5 + -1k = 0 Solving 5 + -1k = 0 Move all terms containing k to the left, all other terms to the right. Add '-5' to each side of the equation. 5 + -5 + -1k = 0 + -5 Combine like terms: 5 + -5 = 0 0 + -1k = 0 + -5 -1k = 0 + -5 Combine like terms: 0 + -5 = -5 -1k = -5 Divide each side by '-1'. k = 5 Simplifying k = 5

Solution

k = {-4, 5}

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