b^2+7ab+6a^2=

Solution for b^2+7ab+6a^2= equation:

Simplifying
b2 + 7ab + 6a2 = 0

Reorder the terms:
7ab + 6a2 + b2 = 0

Solving
7ab + 6a2 + b2 = 0

Solving for variable 'a'.

Factor a trinomial.
(6a + b)(a + b) = 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 + 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
Solution
a = {-0.1666666667b, -1b}