6a^2+37ab+6b^2=0

Solution for 6a^2+37ab+6b^2=0 equation:

Simplifying
6a2 + 37ab + 6b2 = 0

Reorder the terms:
37ab + 6a2 + 6b2 = 0

Solving
37ab + 6a2 + 6b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + b)(a + 6b) = 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 '(a + 6b)' equal to zero and attempt to solve:

Simplifying
a + 6b = 0

Solving
a + 6b = 0

Move all terms containing a to the left, all other terms to the right.

Add '-6b' to each side of the equation.
a + 6b + -6b = 0 + -6b

Combine like terms: 6b + -6b = 0
a + 0 = 0 + -6b
a = 0 + -6b
Remove the zero:
a = -6b

Simplifying
a = -6b
Solution
a = {-0.1666666667b, -6b}