12a^2+20ab+3b^2=0

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Solution for 12a^2+20ab+3b^2=0 equation:


Simplifying
12a2 + 20ab + 3b2 = 0

Reorder the terms:
20ab + 12a2 + 3b2 = 0

Solving
20ab + 12a2 + 3b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + b)(2a + 3b) = 0

Subproblem 1

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

Subproblem 2

Set the factor '(2a + 3b)' equal to zero and attempt to solve: Simplifying 2a + 3b = 0 Solving 2a + 3b = 0 Move all terms containing a to the left, all other terms to the right. Add '-3b' to each side of the equation. 2a + 3b + -3b = 0 + -3b Combine like terms: 3b + -3b = 0 2a + 0 = 0 + -3b 2a = 0 + -3b Remove the zero: 2a = -3b Divide each side by '2'. a = -1.5b Simplifying a = -1.5b

Solution

a = {-0.1666666667b, -1.5b}

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