3k^2+9k=12

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Solution for 3k^2+9k=12 equation:


Simplifying
3k2 + 9k = 12

Reorder the terms:
9k + 3k2 = 12

Solving
9k + 3k2 = 12

Solving for variable 'k'.

Reorder the terms:
-12 + 9k + 3k2 = 12 + -12

Combine like terms: 12 + -12 = 0
-12 + 9k + 3k2 = 0

Factor out the Greatest Common Factor (GCF), '3'.
3(-4 + 3k + k2) = 0

Factor a trinomial.
3((-4 + -1k)(1 + -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 '(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

Solution

k = {-4, 1}

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