6a^2+18ab+12b^2=0

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Solution for 6a^2+18ab+12b^2=0 equation:


Simplifying
6a2 + 18ab + 12b2 = 0

Reorder the terms:
18ab + 6a2 + 12b2 = 0

Solving
18ab + 6a2 + 12b2 = 0

Solving for variable 'a'.

Factor out the Greatest Common Factor (GCF), '6'.
6(3ab + a2 + 2b2) = 0

Factor a trinomial.
6((a + b)(a + 2b)) = 0

Ignore the factor 6.

Subproblem 1

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

Subproblem 2

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

Solution

a = {-1b, -2b}

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