3w^2+12wk-36k^2=0

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Solution for 3w^2+12wk-36k^2=0 equation:


Simplifying
3w2 + 12wk + -36k2 = 0

Reorder the terms:
12kw + -36k2 + 3w2 = 0

Solving
12kw + -36k2 + 3w2 = 0

Solving for variable 'k'.

Factor out the Greatest Common Factor (GCF), '3'.
3(4kw + -12k2 + w2) = 0

Factor a trinomial.
3((-6k + -1w)(2k + -1w)) = 0

Ignore the factor 3.

Subproblem 1

Set the factor '(-6k + -1w)' equal to zero and attempt to solve: Simplifying -6k + -1w = 0 Solving -6k + -1w = 0 Move all terms containing k to the left, all other terms to the right. Add 'w' to each side of the equation. -6k + -1w + w = 0 + w Combine like terms: -1w + w = 0 -6k + 0 = 0 + w -6k = 0 + w Remove the zero: -6k = w Divide each side by '-6'. k = -0.1666666667w Simplifying k = -0.1666666667w

Subproblem 2

Set the factor '(2k + -1w)' equal to zero and attempt to solve: Simplifying 2k + -1w = 0 Solving 2k + -1w = 0 Move all terms containing k to the left, all other terms to the right. Add 'w' to each side of the equation. 2k + -1w + w = 0 + w Combine like terms: -1w + w = 0 2k + 0 = 0 + w 2k = 0 + w Remove the zero: 2k = w Divide each side by '2'. k = 0.5w Simplifying k = 0.5w

Solution

k = {-0.1666666667w, 0.5w}

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